text:
\section{Introduction}

People have been concerned with how to define the energy-momentum and angular momentum of gravitating systems since even before general relativity was born. Different pseudotensors were proposed to describe the local gravitational energy-momentum density. This choice between the different available expressions is one  ambiguity in characterizing the energy-momentum of any local region of space-time. Moreover there is an additional ambiguity: since a pseudotensor is not a covariant object, it leads to values which inherently depend on the reference frame. This feature is actually an inevitable consequence of the fundamental geometric nature of gravity. Mathematically it is due to diffeomorphism invariance (as shown by Noether in her famous paper~\cite{noether}); physically it has been said that the equivalence principle forbids the localization of gravitational energy~\cite{MTW73}. The more modern view is that energy-momentum should be regarded as being \emph{quasi-local} (associated with a closed 2-surface) rather than local. The various quasi-local ideas have been comprehensively reviewed~\cite{Sza09}. There have been many quasi-local proposals, but no consensus.  In fact the quasi-local approach has ambiguities analogous to the two already mentioned.  However, it has been argued that the Hamiltonian approach, in particular the covariant Hamiltonian formalism~\cite{N91,N95,N99,N00,Nester04,N05,N08}, can tame both of these ambiguities, clarifying their geometric and physical nature.    The quasi-local values are then determined by the Hamiltonian boundary term.  A preferred boundary term has been identified; this gives a resolution to the first type of ambiguity. Recent work has finally led to identifying a good procedure for addressing the second type of ambiguity: how to best select the necessary reference values on the boundary~\cite{ae100}. We now test this program on axisymmetric spacetimes, showing that it works well; in particular it yields sensible energy and angular momentum values for the Kerr metric.

Early quasi-local investigations (an outstanding one is the seminal work of Brown and York~\cite{BY93}) naturally explicitly worked out quasi-local energy values for spherically symmetric spacetimes.  As far as we know Matrinez~\cite{Mart94} was the first to consider an axisymmetrical spacetime.  We are concerned with the covariant Hamiltonian formalism; within this approach the quasi-local energy for spherically symmetric spacetime was examined in depth by Wu {\it et al}.~\cite{Wu10,Wu11,Liu11,Wu12}  Here we will now go further: using the results of the covariant Hamiltonian formalism we consider an axisymmetric spacetime, use a new approach to find the best matched reference, and determine both the optimal quasi-local energy and angular momentum.

\section{Covariant Hamiltonian Formalism}

Detailed discussions of the covariant Hamiltonian formalism as developed by our research group can be found in the references~\cite{N91,N95,N99,N00,Nester04,N05,N08}. Here we give a brief summary of some key features.

A \emph{first order Lagrangian 4-form} for a $k$-form field $\phi$ has the form $\mathcal{L}=d\phi\wedge p-\Lambda(\phi,p)$. A vector field $N$ can be regarded as an ``infinitesimal translation''. It generates a local infinitesimal diffeomorphism under which the action associated with $\mathcal{L}$ should be invariant. Using the well-known Lie derivative formula $\pounds_N \equiv di_N + i_Nd$, the associated conserved\footnote{Conserved in the first Noether theorem sense: $d{\cal H}(N) \propto $ field equations.} Noether current 3-form---which is moreover the Hamiltonian---
\begin{equation}
\mathcal{H}(N) := \pounds_{N} \phi \wedge p - i_{N} \mathcal{L} \equiv N^{\mu} \mathcal{H}_{\mu} + d\mathcal{B}(N),
\end{equation}
can be split as indicated into two pieces with distinct roles. The part algebraic in the vector field generates the Hamiltonian equations; from Noether's second theorem concerning local invariance with respect to the choice of $N$ one finds that it is proportional to field equations and thus vanishes ``on shell''. Then the \emph{value} of the Hamiltonian,
\begin{eqnarray} \label{eq1}
E(N, \Sigma) = H(N, \Sigma) = \int_{\Sigma} \mathcal{H}(N) = \oint_{\partial\Sigma} \mathcal{B}(N),
\end{eqnarray}
is {\em quasi-local\/}; it is determined entirely by quantities on the closed 2-surface $S := \partial\Sigma$.

For \emph{any} choice of $N$ this expression defines a conserved quasi-local quantity.  To get a physically meaningful result one needs to have a good way of selecting the specific vectors $N$ that correspond to the quasi-local symmetries that yield the quasi-local energy-momentum and angular momentum/center-of-mass.

It must be noted that the Hamiltonian boundary 2-form ${\cal B}(N)$ can be modified ``by hand''; this would still preserve the conservation property, but change the conserved value. It was shown that in this way the Hamiltonian approach can include the various pseudotensors~\cite{Chang99}. But this ``Noether current'' ambiguity is tamed by the Hamiltonian \emph{boundary variation principle\/}: the boundary term in the variation of the Hamiltonian must be required to vanish.  This determines the related boundary conditions: different boundary terms are associated with different boundary conditions.

Here we consider specifically only Einstein's theory, general relativity (GR).
Our preferred\footnote{At spatial infinity it gives the accepted energy, momentum, angular momentum, and center-of-mass. At null infinity it gives the Bondi energy and energy flux, for small spheres it is a positive multiple of the Bel-Robinson tensor, it has a positivity property, and for spherically symmetric solutions it has the hoop property~\cite{Omur10}.}
boundary term for GR (which corresponds to holding the metric fixed on the boundary) is
\begin{eqnarray}\label{eq2}
16 \pi \mathcal{B}(N) = \Delta\Gamma^\alpha{}_\beta \wedge i_{N} \eta_{\alpha}{}^{\beta} + \overline{D}_{\beta} N^{\alpha} \Delta\eta_{\alpha}^{~\beta}, \label{B}
\end{eqnarray}
where $\eta^{\alpha\beta} := *(dx^\alpha\wedge dx^\beta)$ is the dual form basis, $\Gamma^\alpha{}_\beta = \Gamma^\alpha{}_{\beta\mu}dx^\mu$ is the connection one form, and $\Delta\Gamma := \Gamma - \bar\Gamma$, $\Delta\eta := \eta - \bar\eta$, with the bar refering to non-dynamical reference values
(which are needed only in a neighborhood of the boundary $S$).
The component form of our expression\footnote{An equivalent expression was proposed by Katz, Bi\v{c}\'ak, and Lynden-Bel~\cite{LBKB95,Katz:1996nr}.} is
\begin{eqnarray}
16 \pi \mathcal{B}(N) \label{eq3}
&=& \frac{1}{4} [ N^{\sigma} \sqrt{-g} g^{\gamma\beta} \Delta\Gamma^{\alpha}{}_{\beta\lambda} \delta^{\lambda\tau\rho}_{\alpha\gamma\sigma}
\nonumber\\
&& \quad + \overline{D}_{\beta} N^{\alpha} \Delta(\sqrt{-g} g^{\gamma\beta}) \delta^{\tau\rho}_{\alpha\gamma} ] \epsilon_{\tau\rho\mu\nu} dx^{\mu} \wedge dx^{\nu}.
\end{eqnarray}

The reference values are non-dynamic, they represent the ``vacuum'' or ground state; how to best select these values is our concern here.
The natural reference for dynamic geometry is Minkowski space.  Thus we need to select a specific Minkowski space in the neighborhood of the two boundary.  Any such choice can be specified by selecting some \emph{quasi-Minkowski coordinates}; in fact any four independent functions $y^i,\ i = 0 \dots 3$ defined in a neighborhood of the the 2-boundary $S$ will define a Minkowski metric by $d\bar s^2 = \bar g_{ij} dy^i dy^j, \ \bar g_{ij} = \hbox{diag}(-1,1,1,1)$.
A Killing field of this reference has the form $N^i = N^i_0 + \lambda_0^i{}_j y^j$, where the translation parameters $N_0^i$ and the boost-rotation parameters $\lambda_0^{ij} = \lambda_0^{[ij]}$ are constants.
Using this reference the 2-surface integral  of the Hamiltonian boundary term then gives a value of the form
\begin{equation}
\oint_S {\mathcal B}(N) = - N_0^i p_i(S) + \frac12 \lambda^0_{ij} J^{ij}(S)\,,
\end{equation}
which yields not only a quasi-local \emph{energy-momentum} but also a quasi-local \emph{angular momentum/center-of-mass}. These quasi-local values of course depend on the chosen reference.  As long as the reference approaches at an appropriate rate the flat Minkowski space at spatial infinity, the integrals $p_i(S),\ J^{ij}(S)$ in the spatial asymptotic limit will agree with accepted expressions for these quantities~\cite{MTW73,Regge:1974zd,Beig:1987zz,Szabados:2003yn,Sza06}.

\section{Optimal choice for reference}

To explicitly determine the specific values of the quasi-local quantities one needs some good way to choose the reference.  Minkowski spacetime is the natural choice, especially for asymptotically flat spacetimes~\cite{Kij97}.  However, as noted above, almost any four functions will determine some reference. With such freedom one can still get almost any value for the quasi-local quantities.  This freedom is the quasi-local version of the second type of ambiguity mentioned in the introduction in connection with the reference frame dependence of energy-momentum pseudotensor expressions.

Recently we have proposed a procedure~\cite{ae100} to fix the ``best'' choice of reference.  It has two features: 4D isometric matching\footnote{This was already proposed by Szabados back in 2000 (at a workshop in Hsinchu, Taiwan); he has since extensively explored this idea~\cite{Sza05}.} and energy optimization.  Here we shall show that our procedure works well for a certain class of axisymmetric spacetimes.

\subsection{4D isometric matching}

Previously the program of 4-dimensional isometric matching with energy extremization was explicitly worked out for the most important special case: spherically symmetric spaces (both static and dynamic~\cite{Wu11,Wu12}). Here we turn to what is probably the next most important special case: {\em axisymmetry}. More specifically we will consider Kerr-like metrics, with just one non-vanishing off diagonal term. (The most general axisymmetric metric and the general case without any symmetry are also being investigated; the results of these investigations will be presented in due course.)
Specifically, in terms of suitable spherical coordinates
$x^\mu = \{ x^{0}, x^{1}, x^{2}, x^{3} \} = \{ t, r, \theta, \varphi\}$, we consider metrics of the form
\begin{eqnarray}\label{eq20}
ds^2 = g_{00} dt^2 + g_{11} dr^2 + g_{22} d\theta^2 + g_{33} d\varphi^2 + 2 g_{03} dt d\varphi, \label{metric}
\end{eqnarray}
where the metric components are independent of $\varphi$.
Although it is not the most general metric of an axisymmetric spacetime, it is enough to unveil the property of a non-static spacetime with angular momentum so we can test our ideas.

We assume that the spherical-like coordinates can be chosen such that the boundary of 2-sphere $S = \partial\Sigma$ is given by $t=t_{0}, r=r_{0}$. In general the reference Minkowski metric is determined by four quasi-Minkowski coordinates defined in a neighborhood of $S$ by four suitable functions, $y^i = (T, X, Y, Z)$ of $(t, r, \theta, \varphi)$; from the $y^i$ we find $dy^i = y^i{}_\mu dx^\mu$.

Since the dynamic spacetime metric is not diagonal when expanded in terms of $x^\mu$ the reference metric must likewise allow for off diagonal terms.
In the axisymmetric case one convenient way to achieve this is to use a certain cylindrical form. Let
\begin{eqnarray}\label{eq21}
X = \rho \cos(\varphi + \Phi), \qquad Y = \rho \sin(\varphi + \Phi),
\end{eqnarray}
and assume that $(T, \rho, \Phi, Z)$ are axisymmetric, i.e., they do not depend on $\varphi$.
Then the reference Minkowski metric in a neighborhood of $S$ can be taken to have the form
\begin{eqnarray}\label{eq22}
d \bar{s}^2 &=& \bar g_{ij} dy^i dy^j
\nonumber\\
&=& - dT^2 + dX^2 + dY^2 + dZ^2 = - dT^2 + d\rho^2 + \rho^2 (d\varphi + d\Phi)^2 + dZ^2
\nonumber\\
&=& - ( T_{t} dt + T_{r} dr + T_{\theta} d\theta )^2 + ( \rho_{t} dt + \rho_{r} dr + \rho_{\theta} d\theta )^2
\nonumber\\
&& + \rho^2 ( d\varphi + \Phi_{t} dt + \Phi_{r} dr + \Phi_{\theta} d\theta )^2 + ( Z_{t} dt + Z_{r} dr + Z_{\theta} d\theta )^2
\\
&=& \bar g_{ij} y^i{}_\mu y^j{}_\nu dx^\mu dx^\nu = \bar g_{\mu\nu} dx^\mu dx^\nu. \nonumber
\end{eqnarray}
On the 2-sphere $S$ determined by $t = t_0, r = r_0$ the reference metric is a function of 12 functions of $\theta$, namely\footnote{In this work, we will just deal with a special type of metric with only one cross component. However, (\ref{eq21}), (\ref{eq22}),  and (\ref{isometric})--(\ref{g33}) are quite general, so we can straightforwardly extend our procedure to cover the most general axisymmetric metric.}
\begin{eqnarray}
\{ T_{t}, T_{r}, T_{\theta}, \rho_{t}, \rho_{r}, \rho, \Phi_{t}, \Phi_{r}, \Phi_{\theta}, Z_{t}, Z_{r}, Z_{\theta} \}
\end{eqnarray}
(note that on the 2-sphere $\rho$ determines $\rho_\theta := \partial_\theta\rho$).  We take $T_{r}$ and $T_{\theta}$ as a suitable set of controlling functions on the 2-sphere; then the other 10 can be found algebraically from the 4D isometric matching conditions, $ds^2 \doteq d\bar s^2$, i.e.,
\begin{equation}
g_{\mu\nu} \doteq \bar g_{\mu\nu} := \bar g_{ij} y^i{}_\mu y^j{}_\nu. \label{isometric}
\end{equation}
(Here the notation $\doteq$ means that the relation holds just on the 2-surface $S$.)
For a general metric these relations have the detailed form
\begin{eqnarray}
g_{00} &\doteq& -T_{t}^2 + \rho_{t}^2 + \rho^2 \Phi_{t}^2 + Z_{t}^2, \label{g00} \\
g_{01} &\doteq& -T_{t} T_{r} + \rho_{t} \rho_{r} + \rho^2 \Phi_{t} \Phi_{r} + Z_{t} Z_{r}, \label{g01} \\
g_{11} &\doteq& -T_{r}^2 + \rho_{r}^2 + \rho^2 \Phi_{r}^2 + Z_{r}^2, \label{g11} \\
g_{02} &\doteq& -T_{t} T_{\theta} + \rho_{t} \rho_{\theta} + \rho^2 \Phi_{t} \Phi_{\theta} + Z_{t} Z_{\theta}, \label{g02} \\
g_{03} &\doteq& \rho^2 \Phi_{t}, \label{g03} \\
g_{12} &\doteq& -T_{r} T_{\theta} + \rho_{r} \rho_{\theta} + \rho^2 \Phi_{r} \Phi_{\theta} + Z_{r} Z_{\theta}, \label{g12} \\
g_{13} &\doteq& \rho^2 \Phi_{r}, \label{g13} \\
g_{22} &\doteq& -T_{\theta}^{2} + \rho_{\theta}^{2} + \rho^{2} \Phi_{\theta}^{2} + Z_{\theta}^{2}, \label{g22} \\
g_{23} &\doteq& \rho^2 \Phi_{\theta}, \label{g23} \\
g_{33} &\doteq& \rho^2. \label{g33}
\end{eqnarray}

For our special axisymmetric metric with only one cross term it is easy to see from (\ref{g03}, \ref{g13}, \ref{g23}, \ref{g33}) that
\begin{equation}
\rho \doteq \sqrt{g_{33}}, \quad \Phi_{t} \doteq {g_{03}}/{g_{33}}, \quad \Phi_{r} \doteq g_{13}/g_{33} = 0, \quad \Phi_{\theta} \doteq g_{23}/g_{33} = 0.
\end{equation}
Recalling that $\rho_\theta$ follows from $\rho$, from (\ref{g22}) one can now get\footnote{Consider the spherical coordinate system in $\mathbf{R}^3$.
The relation between the Cartesian coordinates $X, Y, Z$ and the spherical coordinates $r, \theta, \varphi$ is $X = r \sin\theta \cos\varphi$, $Y = r \sin\theta \sin\varphi$, $Z = r \cos\theta$, which is such that $Z_{\theta} = -r \sin\theta$.  Hence the negative root is the reasonable one here, for we wish our procedure to give the usual result for metrics which are flat.}
\begin{equation}
\nonumber Z_{\theta} \doteq - \sqrt{g_{22} + T_{\theta}^2 - \rho_{\theta}^2}.
\end{equation}
This leaves the remaining unknowns $\{ T_{t}, \rho_{t}, Z_{t}, \rho_{r}, Z_{r} \}$ to be determined.
Consider next the pair (\ref{g11}, \ref{g12}):
\begin{eqnarray}
\rho_{r} \rho_{\theta} + Z_{r} Z_{\theta} &\doteq& T_{r} T_{\theta} + g_{12} = T_{r} T_{\theta},
\\
\rho_{r}^2 + Z_{r}^2 &\doteq& g_{11} + T_{r}^2.
\end{eqnarray}
One can first get $Z_{r}$,
\begin{eqnarray}
Z_{r} \doteq \frac{T_{r} T_{\theta} - \rho_{r} \rho_{\theta}}{Z_{\theta}}, \label{Zr}
\end{eqnarray}
and then a quadratic equation for $\rho_{r}$, namely
\begin{eqnarray}
\rho_{r}^2 \left( 1 + \frac{\rho_{\theta}^2}{Z_{\theta}^2} \right) - 2 \frac{\rho_{r} \rho_{\theta} T_{r} T_{\theta}}{Z_{\theta}^2} + \frac{T_{r}^2 T_{\theta}^2}{Z_{\theta}^2} - T_{r}^2 - g_{11} \doteq 0\,.
\end{eqnarray}
Generally $\rho_{r}$ has two solutions,
but one should select the sign that gives a positive value---at least when the dynamical geometry is near flat space.
Once $\rho_{r}$ is determined, $Z_{r}$ can be found from (\ref{Zr}).

As to $T_{t}, \rho_{t}, Z_{t}$, they can now be found through the remaining relations (\ref{g00}, \ref{g01}, \ref{g02}) which are effectively one quadratic and two linear equations:
\begin{eqnarray}
-T_{t}^2 + \rho_{t}^2 + Z_{t}^2 &\doteq& g_{00} - \rho^2 \Phi_{t}^2, \label{00}
\\
-T_{t} T_{r} + \rho_{t} \rho_{r} + Z_{t} Z_{r} &\doteq& g_{01} = 0,
\\
-T_{t} T_{\theta} + \rho_{t} \rho_{\theta} + Z_{t} Z_{\theta} &\doteq& g_{02} = 0.
\end{eqnarray}
From the two linear equations we find
\begin{eqnarray}
\rho_{t} &\doteq& T_{t} \, \frac{T_{r} Z_{\theta} - T_{\theta} Z_{r}}{\rho_{r} Z_{\theta} - \rho_{\theta} Z_{r}}, \label{rhot}
\\
Z_{t} &\doteq& T_t\, \frac{\rho_r T_{\theta} - T_r \rho_{\theta}}{\rho_{r} Z_{\theta} - \rho_{\theta} Z_{r}}. \label{Zt}
\end{eqnarray}
Substituting this into (\ref{00}) gives
a new quadratic equation for $T_{t}$:
\begin{eqnarray}
T_{t}^2 \left[ -1 + \frac{(T_{r} Z_{\theta} - T_{\theta} Z_{r})^2}{(\rho_{r} Z_{\theta} - \rho_{\theta} Z_{r})^2} + \frac{(\rho_{r} T_{\theta} - \rho_{\theta} T_{r})^2}{(\rho_{r} Z_{\theta} - \rho_{\theta} Z_{r})^2} \right] \doteq g_{00} - \rho^2 \Phi_{t}^2.
\end{eqnarray}
This has two solutions, but one should choose the positive value.
Once $T_{t}$ is found, $\rho_{t}$ and $Z_{t}$ can be found from (\ref{rhot}, \ref{Zt}).

Algebraically solving these equations and collecting our isometric matching results together, we have in addition to vanishing $\Phi_r,\ \Phi_\theta$,
\begin{eqnarray}
\rho &\doteq& \sqrt{g_{33}}, \\
\Phi_{t} &\doteq& g_{03}/g_{33}, \\
Z_{\theta} &\doteq& - L_{1}, \\
T_{t} &\doteq& L_{2} L_{3}, \\
\rho_{r} &\doteq& (\rho_{\theta} T_{r} T_{\theta} + {L_{1} L_{3}})/{L_{4}}, \\
Z_{r} &\doteq& ({\rho_{\theta} L_3} - {L_{1} T_{r} T_{\theta}})/{L_{4}}, \\
\rho_{t} &\doteq& L_2 ({L_{1} T_{r} g_{22}} + {L_3 T_{\theta} \rho_{\theta}})/{L_{4}}, \\
Z_{t} &\doteq& L_2 ({\rho_{\theta} T_{r} g_{22}} - {L_{1} L_3 T_{\theta}})/{L_{4}},
\end{eqnarray}
where
\begin{eqnarray}
L_{1} &:=& \sqrt{g_{22} - \rho_{\theta}^2 + T_{\theta}^2}, \\
L_{2} &:=& \sqrt{\frac{g_{03}^2 - g_{00} g_{33}}{g_{11} g_{22} g_{33}}}, \\
L_{3} &:=& \sqrt{T_{r}^2 g_{22} + g_{11} g_{22} + g_{11} T_{\theta}^2}, \\
L_{4} &:=& g_{22} + T_{\theta}^2.
\end{eqnarray}

With 4D isometric matching on the 2-boundary $S$ the second term in our quasi-local expression (\ref{B}) vanishes, so it simplifies considerably to
\begin{equation}
16 \pi \mathcal{B}(N) = (\Gamma^\alpha{}_\beta - \bar\Gamma^\alpha{}_\beta) \wedge i_{N} \eta_{\alpha}{}^{\beta}. \label{B2}
\end{equation}
We will use this expression to determine our quasi-local energy and angular momentum.

\subsection{Energy extremization}
Even with 4D isometric matching the quasi-local values still have a lot of freedom. The value of the energy-momentum can be regarded as a measure of the difference between the dynamical geometry and the reference geometry.  With this in mind it was proposed to look to the critical points of $m^2 := - \bar g^{ij} p_i p_j$~\cite{ae100}.  Here we shall use a simpler expression which should lead to the same answer.
To properly select  $T_{r}$ and $T_{\theta}$ we propose extremizing the quasi-local energy to find the best matching for these embedding functions.

The quasi-local energy is determined by selecting the reference geometry unit timelike Killing vector\footnote{The subscript in $N_{\rm E}$ is used
to denote the vector field for energy}: $N_{\rm E} = \partial_{T}$.
To calculate the quasi-local energy one needs  the components of $N_{\rm E}$ and $\bar\Gamma^\alpha{}_\beta$ in the dynamic spacetime.
The reference connection is determined by pullback from the flat space reference (which vanishes in Minkowski coordinates):
\begin{equation}
\bar \Gamma^\alpha{}_\beta = x^\alpha{}_i (\bar\Gamma^i_{~j} y^j{}_\beta + dy^i{}_\beta) = x^\alpha{}_i dy^i{}_\beta.
\end{equation}
Here $x^\alpha{}_i$ is the inverse of $y^i{}_\alpha$, and the latter is determined from $dy^i = y^i{}_\alpha dx^\alpha$, i.e.,
\begin{eqnarray} \label{reference choice}
\left(
  \begin{array}{c}
    dT \\
    dX \\
    dY \\
    dZ \\
  \end{array}
\right)=\left(
          \begin{array}{cccc}
            T_t & T_r & T_\theta & 0 \\
            \rho_t \cos\xi - \rho \sin\xi \Phi_t\ \ & \rho_r \cos\xi\ \ & \rho_\theta \cos\xi\ \ & -\rho \sin\xi \\
            \rho_t \sin\xi + \rho \cos\xi \Phi_t\ \ & \rho_r \sin\xi\ \ & \rho_\theta \sin\xi\ \ & \rho \cos\xi \\
            Z_t & Z_r & Z_\theta & 0 \\
          \end{array}
        \right)\left(
                 \begin{array}{c}
                   dt \\
                   dr \\
                   d\theta \\
                   d\varphi \\
                 \end{array}
               \right),
\end{eqnarray}
where $\xi = \varphi + \Phi$.

Using these results, the determined values for the components of the vector are
\begin{eqnarray}\label{eq46}
&& N^{t}_{\rm E} \doteq \frac{L_3}{g_{11} g_{22} L_2}, \qquad N^{r}_{\rm E} \doteq - \frac{T_{r}}{g_{11}}, \qquad N^{\theta}_{\rm E} \doteq -\frac{T_{\theta}}{g_{22}},
\nonumber\\
&& N^{\varphi}_{\rm E} \doteq - \Phi_t N^t_{\rm E} = - \frac{g_{03} L_3}{g_{11} g_{22} g_{33} L_2}. \label{N}
\end{eqnarray}
With $N = N_{\rm E}$ the quasi-local boundary term (\ref{B2}) works out to be
\begin{eqnarray}
16 \pi \mathcal{B}(N_{\rm E}) \!&\!\!=\!\!&\! \sqrt{g_{33}} \biggl\{ \frac{2 T_{\theta}}{L_{3}} T_{r\theta} + \frac{2}{L_4} \left[ -\frac{T_{\theta}^2 T_{r}}{L_{3}} + \frac{T_{\theta} \rho_{\theta}}{L_{1}} \right] T_{\theta\theta}
- \frac{g_{11\theta} T_r T_\theta}{L_3 g_{11}}
\nonumber\\
&& \quad + \frac{g_{22\theta}}{L_4} \left[ \frac{T_r T_\theta^3}{g_{22} L_3} + \frac{\rho_\theta}{L_1} \right]
- \frac{2 \rho_{\theta\theta}}{L_{1}} + \frac{2 L_{1}}{\sqrt{g_{33}}} + L_{3} W \biggr\} d\theta \wedge d\varphi, \qquad \label{BE}
\end{eqnarray}
with
\begin{equation}
W := -\frac{1}{g_{11}} \left( \frac{g_{22r}}{g_{22}} + \frac{g_{33r}}{g_{33}} \right).
\end{equation}
Here $g_{22\theta}$ denotes its derivative by $\theta$ and so on.  Also it should be noted that in this expression and in all of the following, to convey our ideas without too many complications, we have additionally assumed that the  metric components in (\ref{metric}) are all time independent.

The quasi-local energy value is the integral of the 2-form $\mathcal{B}(\partial_T)$ (\ref{BE}) over $S$.  The value is a functional of the two control functions $T_\theta, T_r$.  The distinguished values of this energy functional are the ``critical points'', which can be found as the solutions of  the respective variational derivatives, the two Euler-Lagrange equations obtained by variation with respect to the control variables $T_\theta,T_r$.  The respective variational equations are
\begin{eqnarray}\label{eq50}
0 &=& \frac{\partial \mathcal{B}(\partial_T)}{\partial T_{\theta}} - \frac{d}{d\theta} \frac{\partial \mathcal{B}(\partial_T)}{\partial T_{\theta\theta}}
\nonumber\\
&=& \frac{\sqrt{g_{33}}}{L_3} \left[ 2 T_{r\theta} + \left( -\frac{g_{11\theta}}{g_{11}} + \frac{g_{33\theta} T_{\theta}^2}{g_{33} L_{4}}\right) T_{r} + \frac{2 L_{1} L_3 T_{\theta}}{\sqrt{g_{33}} L_{4}} + g_{11} W T_{\theta} \right], \label{ELtheta}
\\
\label{eq51}
0 &=& \frac{\partial \mathcal{B}(\partial_T)}{\partial T_{r}} - \frac{d}{d\theta} \frac{\partial \mathcal{B}(\partial_T)}{\partial T_{r\theta}}
\nonumber\\
&=& \frac{\sqrt{g_{33}}}{L_3} \left[ -2 T_{\theta\theta} + \left( \frac{g_{22\theta}}{g_{22}} - \frac{g_{33\theta}}{g_{33}} \right) T_{\theta} + g_{22} W T_{r} \right]. \label{ELr}
\end{eqnarray}
The second relation can be used to eliminate $T_r$ from the first relation.  The result is a quasi-linear (but highly nonlinear) second order equation for $T_\theta$.  For such equations there is generally little hope of finding any analytic solution.  However, this case is still rather special: there is one quite obvious simple solution that applies to all of these Kerr-like metrics, namely the trivial solution $T_r = 0 = T_\theta$.

For the simple solution $T_r=0=T_\theta$ the vector field takes the simpler form
\begin{eqnarray}\label{eq58}
N^{t}_{\rm E} = \frac{1}{T_{t}} = \sqrt{\frac{g_{33}}{g_{03}^2 - g_{00}g_{33}}}, \quad N^{\varphi}_{\rm E} = -\frac{g_{03}}{g_{33}} N^t_{\rm E}, \quad N^{r}_{\rm E} = 0, \quad N^{\theta}_{\rm E} = 0.\label{vector}
\end{eqnarray}
This vector is orthogonal to the constant $t$ hypersurface; physically it can be identified with the \emph{static\/} observer on the boundary.

From (\ref{BE}) with $T_\theta=0=T_r$, on the $t,r$ constant 2-surface of any axisymmetric time independent metric of the form (\ref{eq20}), our optimal boundary term for the quasi-local energy is
\begin{eqnarray}\label{eq4}
\mathcal{B}_{\rm E} &=& \frac{\sqrt{g_{33}}}{16\pi} \Bigl\{ -\Bigl( \frac{\partial_{r} g_{22}}{g_{22}} + \frac{\partial_{r} g_{33}}{g_{33}} \Bigr) \frac{\sqrt{g_{22}}}{\sqrt{g_{11}}}
\nonumber\\
&+& \frac{(\partial_{\theta} g_{22})(\partial_{\theta} g_{33}) - 2 g_{22} (\partial_{\theta\theta} g_{33}) + 4 g_{22}^2}{g_{22} \sqrt{4 g_{33} g_{22} - (\partial_{\theta} g_{33})^2}} ~\Bigr\} d\theta \wedge d\varphi. \label{optimalenergy}
\end{eqnarray}

Turning to the quasi-local angular momentum, note that it can have only one non-vanishing component.  To select this component from our quasi-local boundary term (\ref{B2}) the appropriate vector field is the \emph{reference rotational Killing field}, $N_{\rm AM} = X \partial_{Y} - Y \partial_{X}$, around the axis. In the dynamic spacetime, this vector field works out to have a very simple form, namely
\begin{eqnarray}\label{eq54}
N_{\rm AM} = \partial_{\varphi},
\end{eqnarray}
and it is in fact the \emph{axisymmetric Killing field} for the metrics considered.
For the choice of $N_{\rm AM} = \partial_{\varphi}$, which implies that the only non-vanishing vector component is $N^{\varphi} = 1$, the boundary expression (\ref{B2}) takes the specific form
\begin{eqnarray}\label{AM N3=1}
16 \pi \mathcal{B}_{\rm AM} = \sqrt{-g} (g^{1\beta} \Delta\Gamma^{0}{}_{\beta3} - g^{0\beta} \Delta\Gamma^{1}{}_{\beta 3} ) d\theta \wedge d\varphi.
\end{eqnarray}
Using the reference choice (\ref{reference choice}), a computation shows that the reference connection contribution vanishes, so the boundary term depends only on the dynamical part:
\begin{eqnarray}\label{AM N3=1 dyn}
16 \pi \mathcal{B}_{\rm AM} &=& \sqrt{-g} (g^{11} \Gamma^{0}{}_{13} - g^{00} \Gamma^{1}{}_{03} - g^{03} \Gamma^{1}{}_{33}) d\theta \wedge d\varphi
\nonumber\\
&=& \sqrt{-g} g^{11} (g^{00} \partial_{r} g_{03} + g^{03} \partial_{r} g_{33}) d\theta \wedge d\varphi. \label{J}
\end{eqnarray}

\section{Detailed results}

To see whether this simple choice is really a good choice---maybe even the best---for determining the reference we examined some physically meaningful special cases.

\subsection{Minkowski metric}
For the Minkowski metric it is easy to see that there is actually a simple non-trivial solution to the two embedding equations (\ref{eq50}) and (\ref{eq51}), namely
\begin{equation}
T_{r} = -\lambda \cos\theta, \qquad T_{\theta} = \lambda r \sin\theta , \label{boostedref}
\end{equation}
with a constant $\lambda$. With this choice the vector field (\ref{N}) corresponds to that of a constant boost along the axis:
\begin{eqnarray}\label{eq53}
N^{t}_{\rm E} = \sqrt{\lambda^2 + 1}, \quad N^{r}_{\rm E} = \lambda \cos\theta, \quad N^{\theta}_{\rm E} = -\frac{\lambda\sin\theta}{r}, \quad N^{\varphi}_{\rm E} = 0.
\end{eqnarray}
For all $\lambda$ the value of the optimal boundary expression (\ref{BE}) and the associated energy vanish:
\begin{eqnarray}\label{eq6}
\mathcal{B}(N_{\rm E}) = 0, \qquad {E} = \oint \mathcal{B}(N_{\rm E}) = 0.
\end{eqnarray}
This is sensible: a sphere in Minkowski space has vanishing energy, and for a boosted observer it still has vanishing energy.  It should be noted that, because we constrained everything to be axisymmetric, we did not find general boost freedom---only boost freedom along the axis.
Because the Minkowski geometry has this symmetry, naturally our procedure cannot find a unique reference.  Furthermore, because the symmetries of Minkowski are  known we need not look further for any other solutions to our equations to find a good reference.

It is easy to verify that, just as it should, for any $\lambda$ our expression also gives vanishing angular momentum for Minkowski space.

\subsection{Schwarzschild metric}
We next consider the Schwarzschild metric.  To identify the desired physical solution, consider first the limit for small $m$ and/or large $r$; then the physical solution should approach the one just found for Minkowski space.  But expressions of the form (\ref{boostedref}) can only solve the equations (\ref{ELtheta},\ref{ELr}) for the Schwarzschild metric for the trivial value $\lambda=0$.  This is the physical solution we want to use for our preferred reference, both for this limit and for more general values of $m$ and $r$.  With vanishing $T_r,T_\theta$, from (\ref{vector}) for the Schwarzschild metric is that of a static observer:
\begin{eqnarray}\label{eq57}
N^{t}_{\rm E} = 1/\sqrt{-g_{00}},
\quad N^{\varphi}_{\rm E} = 0, \quad N^{r}_{\rm E} = 0, \quad N^{\theta}_{\rm E} = 0,
\end{eqnarray}
which is only meaningful for $-g_{00} = 1 - 2m/r > 0$, i.e., outside the horizon.  This strategy cannot be used to find a reference for the dynamic region inside the horizon (alternatives that can cope with the interior region have been discussed elsewhere~\cite{Wu10,Wu11,Wu12}).
For this case the energy boundary term (\ref{optimalenergy}) and the associated energy values are
\begin{eqnarray}
&& \mathcal{B}_{\rm E} = \frac{4r}{16\pi} (1 - \sqrt{1 - {2m}/{r}}) \sin\theta d\theta \wedge d\varphi,
\nonumber\\
\label{eq8}
&& {E} = \oint \mathcal{B}_{\rm E} = r (1 - \sqrt{1 - {2m}/{r}}) = \frac{2m}{1 + \sqrt{1-{2m}/{r}}}.
\end{eqnarray}
This is the well known quasi-local energy first found by Brown and York~\cite{BY93}.

From (\ref{J}) it is easy to see that, as it should, our quasi-local angular momentum vanishes for the Schwarzschild metric.

\subsection{Kerr metric}
Let us now consider specifically the Kerr metric. In terms of the convenient Boyer-Linquist coordinates, the Kerr solution is
\begin{eqnarray}
ds^2 &=& - \frac{(\Delta - a^2 \sin^2\theta)}{\Sigma} dt^2 + \frac{\Sigma}{\Delta} dr^2 + \Sigma d\theta^2
\nonumber\\
&&-\frac{4 m a r \sin^2\theta}{\Sigma} dt d\varphi + \left[ \frac{(r^2 + a^2)^2 - \Delta a^2 \sin^2\theta}{\Sigma} \right] \sin^2\theta d\varphi^2, \label{Kerr}
\end{eqnarray}
where $\Sigma(r, \theta) := r^2 + a^2 \cos^2\theta$, $\Delta(r) := r^2 - 2 m r + a^2$.
For the Kerr metric the special relations $g_{22}/g_{11} = \Delta$ and $g_{03}^2 - g_{00} g_{33} = \Delta\sin^2\theta$ hold.

By the same argument used for the Schwarzschild metric, we take as our desired reference the trivial solution $T_\theta = 0 = T_r$.  The associated displacement vector field from (\ref{vector},\ref{Kerr}) has a well-known form.
For the Kerr metric the expression (\ref{optimalenergy}) is too complicated to find an analytical result.  So we turn to other procedures.  We first find an approximate quasi-local energy for a slowly rotating Kerr black hole, then we present a numerical evaluation.

\subsubsection{When $|a| \ll m$}
With the Kerr metric values the slow rotation approximation is
\begin{eqnarray}\label{eq12}
\mathcal{B}_{\rm E} &\approx& \frac{1}{16\pi} \Biggl\{ 4 r \Bigl( 1 - \sqrt{1 - \frac{2m}{r} + \frac{a^2}{r^2}} \Bigr) \sin\theta
\nonumber\\
&& + \Bigl[ \Bigl( \frac{2 \sin\theta \cos^2\theta}{r} + \frac{2 m \sin^3\theta}{r^2} \Bigr) \sqrt{1 - \frac{2m}{r} + \frac{a^2}{r^2}}
\nonumber\\
\label{eq13}
&& + \frac{2 \sin^3\theta}{r} - \frac{20 m \sin\theta \cos^2\theta}{r^2} + \frac{8 m \sin\theta}{r^2} \Bigr] a^2 \Biggr\} d\theta \wedge d\varphi,
\nonumber\\
\label{eq14}
{E} &=& \oint \mathcal{B}_{\rm E}
\nonumber\\
&\approx& \!\! r \Bigl( 1 - \sqrt{1 - \frac{2m}{r} + \frac{a^2}{r^2}} \Bigr) + \frac{(1 + \frac{2m}{r}) \sqrt{1 - \frac{2m}{r} + \frac{a^2}{r^2}} + 2 + \frac{2m}{r}}{6r} a^2. \qquad
\end{eqnarray}
Our quasi-local energy value for the Kerr metric using the slow rotation approximation turns out to be identical with that found by Martinez from the Brown-York quasi-local expression~\cite{Mart94}.

\subsubsection{General cases: $0\leq|a|\leq m$}
On the $t,r$ constant closed 2-surface we calculated numerically the value of our quasi-local energy with
our best matched reference for the Kerr metric.
In Figure~1 we show how the  quasi-local energy in units of $m$ (i.e., $E/m$) depends on $a/m$ and $r/m$.  Some of the numerical data is presented in Table 1.
\begin{figure}[pb]
\begin{center}
  \includegraphics[trim=20 20 20 20, clip,width=3in,angle=270]{3d}\\
  \vspace*{8pt}
  \caption{A plot of our Kerr quasi-local energy for $r\geq2$, with all the quantities given in units of $m$.  No matter what the value of $a\le 1$, as $r$ approaches infinity, $E$  approaches $1$, as is well known. The highest point corresponds to the Schwarzschild case, with $E=2$ at $r=2$. For any $r$, the larger $|a|$ is, the smaller $E$ is. }
  \end{center}
\end{figure}

\begin{table}
\caption{The quasi-local energy ${E}$ dependance on $|a|$ and  $r$.}
{\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
  ${E}/m$&$r/m=2$&$r/m=3$&$r/m=10$&$r/m=20$&$r/m=50$\\\hline
  $|a|/m=0.0$ & 2.00000000 & 1.26794919 & 1.05572809 & 1.0263340 & 1.0102052  \\\hline
  $|a|/m=0.1$ & 1.90258182 & 1.26708057 & 1.05571462 & 1.0263325 & 1.0102050  \\\hline
  $|a|/m=0.2$ & 1.81063676 & 1.26449931 & 1.05567426 & 1.0263278 & 1.0102048  \\\hline
  $|a|/m=0.3$ & 1.72457134 & 1.26027757 & 1.05560706 & 1.0263200 & 1.0102042  \\\hline
  $|a|/m=0.4$ & 1.64468939 & 1.25453045 & 1.05551316 & 1.0263091 & 1.0102036  \\\hline
  $|a|/m=0.5$ & 1.57117096 & 1.24740880 & 1.05539271 & 1.0262951 & 1.0102028  \\\hline
  $|a|/m=0.6$ & 1.50406598 & 1.23909055 & 1.05524594 & 1.0262779 & 1.0102017  \\\hline
  $|a|/m=0.7$ & 1.44330154 & 1.22977111 & 1.05507309 & 1.0262577 & 1.0102004  \\\hline
  $|a|/m=0.8$ & 1.38869944 & 1.21965415 & 1.05487447 & 1.0262344 & 1.0101990  \\\hline
  $|a|/m=0.9$ & 1.33999980 & 1.20894300 & 1.05465044 & 1.0262080 & 1.0101974  \\\hline
  $|a|/m=1.0$ & 1.29688677 & 1.19783368 & 1.05440138 & 1.0261786 & 1.0101956  \\\hline
\end{tabular}}
\end{table}

\subsubsection{Kerr angular momentum}

Evaluating (\ref{J}) explicitly for the Kerr metric (\ref{Kerr}) we find that the exact boundary expression for our quasi-local angular momentum on the $t,r$  constant 2-surface works out to
\begin{eqnarray}
16 \pi \mathcal{B}_{\rm AM} &=& \frac{2 m a \sin^{3}\theta}{\Sigma} [ (1 - 2 r^{2}/\Sigma) (r^{2} + a^{2}) - 2 r^{2} ]\, d\theta \wedge d\varphi
\nonumber\\
&=& - \frac{2 m a [ 3 r^4 + r^2 a^2 (1 + \cos^2\theta) - a^4 \cos^2\theta ] {\sin^3\theta}}{(r^2 + a^2 \cos^2\theta)^2} ~d\theta \wedge d\varphi. \qquad \label{KerrBAM}
\end{eqnarray}
Hence the one non-vanishing component of our quasi-local angular momentum for the Kerr metric is
\begin{eqnarray}
\label{eq11} {J_\varphi} = \oint \mathcal{B}_{\rm AM} = \frac{m a \cos\theta (3 r^2 - r^2 \cos^2\theta + a^2 + a^2 \cos^2\theta)}{4 (r^2 + a^2 \cos^2\theta)} \Big|^{\pi}_{0} = - m a.
\end{eqnarray}

It is amazing that our quasi-local angular momentum turns out to have a simple natural $r$-independent value, even though the boundary term ${\cal B}(\partial_\varphi)$ (\ref{KerrBAM}) is a not so simple function of $r$.

\section{Conclusion}

Our approach to identifying the quasi-local energy and angular momentum for gravitating systems is via the covariant Hamiltonian formalism.
How to choose the reference geometry and the evolution vector that appear in the Hamiltonian boundary term have been outstanding issues in the quasi-local program. Minkowski geometry and its associated Killing fields are the natural choice, but one actually needs a program for selecting a specific Minkowski geometry on the boundary.
Here for axisymmetric metrics we show that this can be accomplished using an appealing program: \emph{four}-dimensional isometric matching on the boundary 2-surface and energy optimization.

Exact 4D isometric matching includes 2-surface isometric matching.  In general this is the problem of embedding a closed 2-surface into Minkowski space.  Wang and Yau have carefully considered this problem in connection with their quasi-local energy investigations~\cite{WY09PRL,WY09CMP}.  The problem generally involves the solution of a nonlinear partial differential equation.  Although they proved an existence and uniqueness theorem, it does not seem possible to find a general analytic formula for the embedding functions.  However, for the axisymmetric case  considered here the situation is quite different.
The 2-surface isometric matching, and indeed the whole 4D isometric matching is in this case essentially a simple \emph{algebraic} problem. With 4D isometric matching the choice of Minkowski reference on the boundary still has two degrees of freedom.

To determine the remaining two degrees of freedom we have proposed energy optimization.
Our energy optimization procedure in the axisymmetric case leads to a pair of first order quasi-linear \emph{ordinary\/} differential equations.
A certain class of Kerr-like metrics fortunately have a simple analytic solution (the trivial solution) to these non-linear energy optimization equations.  One cannot expect to find such simple analytic solutions in more general cases, such as a dynamical metric with more non-vanishing cross terms, a time dependent metric, or for some other 2-surface $S$ described by a formula like $R = R(r,\theta) = \hbox{constant}$.  That we can have our solution of trivial embedding variables can be attributable to the fact that the Boyer-Lindquist coordinate $r$ has a special significance for these Kerr-like geometries, and the constant $r$ surfaces are thus quite special and meaningful.

For the considered metrics it is noteworthy that our optimal timelike vector field turned out to be hypersurface orthogonal, corresponding to a static observer. Our quasi-local expression with  best matched reference gives for Minkowski space, as expected, vanishing energy and angular momentum.  For the Schwarzschild metric it gives the well-known energy value first found by Brown and York along with vanishing angular momentum.

We found the exact analytic formula for our optimal quasi-local energy boundary term for these Kerr-like metrics on the surface $r=\hbox{constant}$.
For the Kerr metric in the slow rotation approximation our quasi-local energy agrees with that  found by Martinez using the Brown-York quasi-local expression.
We plotted our Kerr quasi-local energy and note that it is a decreasing function of $|a|$.  At present we have no physical understanding as to why this is the case.

For these Kerr-like metrics we found our optimal quasi-local angular momentum boundary term.  Our quasi-local angular momentum for the Kerr metric worked out to be an unexpectedly simple but satisfying constant value ($-ma$).
This may again be attributed to the chosen 2-surface $S$, which is given by a constant value of the Boyer-Lindquist coordinate $r$.  It is another indication of the special significance of this coordinate for these metrics.  Our quasi-local angular momentum would not be so simple for closed surfaces of the form $R=R(r,\theta)=\hbox{constant}$.

Encouraged by these results, the application of these ideas is being extended to both general axisymmetric metrics and completely general metrics.

\section*{Acknowledgments}
This work was supported by the National Science Council of the R.O.C. under the grants NSC 101-2112-M-008-006 and 99-2112-M-008-005-MY3, the Institute of Physics, Academia Sinica, and the National Center of Theoretical Sciences (NCTS).

redpajama_set_name: RedPajamaArXiv


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Director: Julien Magnat
For a movie called "Bloody Mallory" there's a surprising lack of blood in this French supernatural action flick. The movie is like the bastard child of Buffy the Vampire Slayer and a Japanese cult horror flick, like Tokyo Gore Police…without the gore. And, interestingly enough, there are shout outs to Lovecraft in the film.
The film follows the exploits of the titular (pun intended) Mallory and her sidekicks, a transsexual named Vena Cava, and a mute pre-teen telepath named Talking Tina who can possess the bodies of other people or animals. Mallory also has help from her dead demon husband, who has rather well done glowing red eyes for a low budget flick. In fact, all of the make up effects are pretty good, easily rivaling Buffy or Doctor Who (in fact, I'm pretty sure I spotted a few Who extras). Mallory and her band have to stop the fallen angel, Abbadon, from releasing the other fallen angels, but he happens to be the Pope…yeah, I'm not going to explain that one.
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One of the most surprising and welcome bits of the film is Valentina Vargus as the evil vampiress. Ms. Vargus, best known as "the girl/the Rose" in Name of the Rose and Angelique in Hellraiser Bloodlines, was apparently reluctant to be in the film, but she's very good as the sexy vampire assistant to the Pope.
There's really no explaining this film properly. From Vena Cava's dildo nunchucks to Mallory's revealing zip up top, this film is just…weird. A good kind of weird, though, and amusing at times. For a French film, there's no nudity, no gore, some blood, but not much, and the violence is mostly not shown. In fact, other than some strong language (Mallory wears gloves that spell out on the fingers, "FUCK EVIL"), this film would be kid friendly.
It's worth a watch, if for no other reason to see how bizarre the whole thing is.

redpajama_set_name: RedPajamaCommonCrawl


You may remember that in October, I was interviewed by Napalm Nick on his blog. This was a very fun experience. Now Nick has interviewed another friend of mine, who often goes by that name SomethingLikEvil. I think that you'll find this interview to be a very interesting read.
Now, you may be asking yourself "why are you linking us to this article when it has nothing to do you?" Well, as side from plugging my friend's site, the person that he's interviewing is going to be releasing a book soon and this book (The Devil's Soapbox) is a project that I was able help with. You see, yours truly edited and created the cover art for this tome. I will be providing more information about The Devil's Soapbox, in future Sell Out Copies.
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text:
5 seen on rooftops of Ithaca businesses arrested; police probe link to break-ins
by Jeff Stein August 17, 2014 August 17, 2014
A worker at Angelos Dry Cleaners, which has been burglarized twice.
Ithaca, N.Y. — Two people seen on the roof of Firehouse Subs and three people seen on the roof of Home Depot were arrested in separate incidents this weekend amid a rash of break-ins at Ithaca businesses.
Ithaca police have been trying to catch the burglar or burglars responsible for more than 10 break-ins at area stores over the last few weeks.
None of the five people arrested this weekend in the rooftop incidents has been charged in connection with the burglaries.
However, "the City of Ithaca has had a number of commercial burglaries reported of late, so responses to incidents of this nature are significant," Lt. Scott N. Garin said in a news release.
Here's the account police gave of each burglary:
1 — Firehouse Subs at 740 South Meadow Street
Firehouse Subs had been burglarized on Aug. 8 and Aug. 12. Police were called there again Friday night around 11:30 p.m. for a report of people on the roof of the store.
There they found two men and arrested them.
"Access to the business did not appear to have been made and nothing was reported to have been stolen from within," Lt. Garin said.
Police say one of the men was found with drugs and charged with third-degree criminal possession of a controlled substance, a felony, and the misdemeanor of criminal trespass. The second man was charged with criminal trespass.
Both men have been released.
2 — Home Depot at 410 Elmira Road
At around 11:55 p.m., police were called to Home Depot for a report of people on the roof.
"This area has been the site of a number of commercial burglaries this year," Garin said.
Ithaca police caught three people fleeing the area and interviewed two people in a vehicle nearby.
The three seen fleeing — two men and an underage teenager — were arrested and charged with third-degree criminal trespass. They have not also not been identified in connections with the Elmira Road burglaries.


text:
Property clearing for…
Property clearing for new library construction
With the razing of the former Reed Center building in downtown Martin, the property will soon be cleared for construction on the new Martin Public Library.
The multi-million dollar 21st Century library will be located on the corner of North Lindell and University streets.
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https://www.thunderboltradio.com/wp-content/uploads/2019/09/NEWS455C.mp3
Dr. Dunagan says there are three key points on the importance of a new 21st Century library.
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TIME AND COSTS – TAKING CONTROL OF YOUR INTERNATIONAL ARBITRATION
While the economic crisis has had an impact on international arbitration, the writing was on the wall even before its full financial toll was realised across global markets. From the perspective of an institution that provides a full range of conflict management services, the message was all too clear that users of international arbitration and mediation were concerned with the escalating time and costs of the alternative dispute resolution (ADR) mechanisms they were selecting for their cross-border contracts. In response, the International Centre for Dispute Resolution (ICDR), which is the international division of the American Arbitration Association (AAA), has taken steps to address these concerns and these efforts have resulted in providing users with additional services and options available to them for their dispute resolution processes.
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The Federal Circuit's Berkheimer v. HP decision has brought the patent eligibility statute, 35 U.S.C. § 101, back into the headlines. In October 2016, Ryan Truesdale wrote on this blog that "the statute addresses the basic question of 'is this invention the type that is patentable.'" The Federal Circuit's decision in the Berkheimer case finally provides some degree of clarity and the USPTO, after several false starts, has finally set out clear directions for the examiners and the PTAB.
The USPTO's Berkheimer memo states that a rejection under 35 U.S.C. § 101 requires an examiner to provide written support that the claimed subject matter is "well-understood, routine, and conventional to a skilled artisan at the time of the patent is a factual determination." Berkheimer v. HP Inc., 881 F.3d 1360, 1369 (Fed. Cir. 2018). One benefit of the ruling in the Berkheimer case is that facts will always matter. Examiners must use facts from citations to declare an application ineligible. Citations can be used from court decisions, publications, and/or an official notice statement(s). The memo describes "an appropriate" publication as a "book, manual, review article, or other source that describes the state of the art discusses what is well-known and common use in the relevant industry." As a gift to applicants, the memo states that when an applicant responds to an ineligibility determination, the examiner must provide explicit support, citing books, manuals, review articles, or case decisions, thereby effectively negating ineligibility rejections based solely upon official notice.
The Berkheimer memo drew from the Federal Circuit Court's decision in that case as to "whether the purported improvements were more than well-understood, routine, conventional activity previously known in the industry." Id., at 1370-71. "The mere fact that something is disclosed in a piece of prior art, for example, does not mean it was well-understood, routine, and conventional." Id., at 1369. Applicants following the directives in the Berkheimer memo will be more successful in overcoming ineligibility determinations than in the USPTO's previous directives under the Supreme Court's decision in Alice Corp. Pty. Ltd. v. CLS Bank International, 134 S. Ct. 2347 (2014). There, the Supreme Court invalidated patent claims because abstract ideas were declared unpatentable by the court without "something more".
In sum, the USPTO's Berkheimer memo provides avenues for overcoming abstract idea ineligibility determinations. Examiners will need to provide evidence to support their contentions. Finally, the USPTO has provided safeguards against arbitrary, anecdotally-based decision making by examiners and the PTAB.


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NHF Professional Memberships
National Headache Foundation memberships are available to health care professionals interested in receiving additional benefits. Professional members can receive our educational brochures to display in their office.
Professional members also receive a $200 discount on the Certificate of Added Qualification in Headache Medicine (AQH) exam. Learn more about the AQH exam.
Click on the appropriate membership level for you:
Healthcare Membership — $75 annually
Subscription to HeadFirst, the monthly e-newsletter from the NHF
Educational brochures to distribute to patients
Discount on AQH exam fee
Physician Membership — $125 annually
Listing on NHF Healthcare Provider Finder page
Physician membership is available to licensed MDs and DOs. Please send or fax a copy of your C.V. and current state license.
If you do not want to be listed on our online search database, please let us know when you send your C.V. and state license.
Mail: National Headache Foundation | 820 N. Orleans, Suite 201 | Chicago, IL 60610
Phone: 312-274-2650 or 888-643-5552 (Toll Free)
*The National Headache Foundation is a 501(c)(3) tax exempt organization.
Rolling Call for Research Proposals
The National Headache Foundation supports research in the field of headache and pain as part of our mission, which also includes offering education and information to headache sufferers. The NHF has provided more than $2 million in 215 research grants to physicians and scientists working in the field of headache medicine. These research studies have resulted in more than $10 million of subsequent funding from the National Institutes of Health.
The Foundation intends to award one or more research grants in its 2020 funding cycle to the best proposal(s) submitted during one of the allotted time periods of our rolling/continuous RFP. Experienced researchers and research organizations are encouraged to apply for an award by describing a worthy project in 12 type-written pages or less, including a description of the project, methods, statistical plan, key personnel to be involved, and a proposed budget detailing how the funds will be used to complete said project in a timely fashion. Brief letters of support from collaborators and biosketches of key personnel will be accepted as supplemental documents to the proposal. At this time we are pleased to announce that the foundation intends to award a total of $200,000 for the 2020 cycle. The actual number and amounts of awards granted will all be at the discretion of the research steering committee whose decisions are final. Pre-proposal contacts to discuss the NHF's vision and research priorities are welcome via email to Dr. Timothy R. Smith, research steering committee chair, at [email protected]
Preference will be given to proposals for projects which:
Could be completed in one year or less
Propose research which is patient-centric and includes patient input into the design
Emphasizes and leads to results which could have real-world application for headache sufferers in the near-term
Have potential or plans for supplemental, matching, sustainable, or in-kind funding sources
Provide answers or solutions to real-world problems dealing with access to care, implementation of innovations in headache management, or develop new ways of understanding the plight of those who suffer from severe headache disorders
Are of sufficient rigor and quality to be worthy of publication in a peer-reviewed journal
The decision regarding the award will be made by the NHF Research Steering Committee after review of all proposals by its members at quarterly proposal review meetings. Proposals received by the last day of each quarter (March 31, June 30, September 30, and December 31) will be reviewed and decisions announced before the last day of the subsequent quarter. The awards will be determined by a majority vote of the committee members and the decision will be final. Should the proposals received not meet the approval of the committee, the funding will be carried over to the next quarter continually. Once all funds for the current year are committed/awarded, further submissions will be queued until the next year's funding is announced and made available.
Inquiries, questions, or comments should be submitted by email to the Research Committee Chair, Dr. Timothy R. Smith @ [email protected] Otherwise, proposals received in complete form as described above by 5 pm (CST) on the final day of each quarter will be considered for awards as long as funding remains available. (We are currently not accepting grant proposals)


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'Oxygen' ending explained: Director explains Netflix's new sci-fi movie
"What keeps people fighting in their darkest moments?"
Dais Johnston
5.13.2021 12:00 AM
Oxygen is a much bigger story than it seems. The new French sci-fi thriller on Netflix begins as just the tale of Liz, a woman who wakes up in a cryogenic pod with no memory and a slowly declining amount of oxygen. But by the end, the story is much larger than Liz or even her life's work. It's the story of the human race trying to cling to survival in an inhospitable world.
Confused by the ending? We're here to help. Read on to learn how the film's director interprets it.
Warning! Major spoilers for Oxygen ahead!
Oxygen director Alexandre Aja signed onto the film three years after pre-production started, but he has a deep love of the story and how the survival elements echo the human spirit especially during this global pandemic.
"I've always been fascinated by how we somehow transcend our limits," Aja tells Inverse. "What keeps people standing when they're probably going to die? What keeps people fighting in their darkest moments?"
We see those questions answered explicitly as Liz records an audio message for her husband Leo just as she's about to run out of air. She tells him she'll cherish the memories she has of them, even if they've never met each other. That spurs her to find a solution to her problem and save her life.
Liz and a dying Leo in a flashback on Earth. Netflix
As it turns out, Liz has only been alive for 102 minutes. She's one of 10,000 Omicrons, genetically engineered clones created to populate a new planet for the regeneration of the human race. Liz's husband, Leo, died on Earth of a deadly virus. But the Omicron version of him survives, stuck in stasis for when the ship filled with pods arrives on their new planet, Wolf 1061c.
It's a great twist ending for a science-fiction movie, but there's more real science in it than you may think. Wolf 1061c is a real planet, tidally locked so one side is always illuminated, one side always dark. The thin strip in between the two could be habitable, but the star is 13.8 light-years away, therefore creating the need for cryogenic stasis for the long journey.
But is the journey successful? At the end of the film, we do see Leo and Liz embracing on a beach with a nearby planet looming overhead. Though technically, these aren't really Leo and Liz. Their real love story ended when Leo died back on Earth, leaving Liz to grow old and continue her research on memory transplanting.
Leo and Liz in the last shot of Oxygen. Netflix
Therefore, Oxygen has two endings: a tragedy caused by a pandemic, and a new beginning for both the connection between Leo and Liz and the human race as a whole. But which ending does Aja intend to be the "real" one?
"It's a weird thing," he says, "because I want to be on the optimist side and I want to believe that actually their love story succeeded, but at the end, I think that the movie is really a battle."
In a story where two versions of the same characters can co-exist, maybe two different endings can too. Aja leaves it up to the viewer to choose how they think the film ends.
"It's almost like a life after death," says Aja. "Both characters are dead to the original characters. I don't know exactly who those two people are and if they're really themselves, or just a fake version of themselves. I think that everyone will have a different interpretation of what it means."
Oxygen is now streaming on Netflix.


I hope November found you well my friend. I thought you might be interested in some of my experiments in mental weather manipulation. I don't know if I read about it first on your site or another one but I had come across a Prayer used by a woman that was based upon a water prayer by Masaru Emoto for cleansing and purifying drinking water. I ended up modifying the prayer to my own end but have since replaced most of it with intent and generally never use the prayer anymore as my energy work, intent and raising my vibrational awareness to that of the clouds and my environment seem to work equally as well. The later technique was relayed to me by an extremely adept psychic who is both prevalent in weather and time manipulation. She is able to walk into the rain and have it stop raining around her and whomever she is with. My first experiment with eliminating the chemtrails came while I was sitting on my back porch watching a large storm system move in following spray trails about 6 months back. I watched as the trails came in followed lock step by this massive storm system. The sky over my house became pitch black, I picked a spot directly over the house and said the prayer calling on Sylphs to come in the area and remove the negative frequency in the clouds. I said the prayer three times and focused intently on the cloud region directly overhead, within 15 minutes I had punched a huge hole in the storm cloud only directly over the house, almost a perfect circle, the sun was shining through, mean while everywhere else around this circle was dark clouds, thunder, lightening and rain. My jaw dropped. This was one hell of a first experiment. I ended up leaving my house not too long after and went to a friends house about 15 minutes away. When I came back a little over an hour later, imagine my surprise when I got home to find the whole region around my house dark except for the spot over my house, the sun still shining down.
I keep this prayer in my wallet. Over the months I have been experimenting with different techniques to eliminate these clouds. I live close to the beach and I generally try to get out there at least once a weekend if at all possible to soak up the sun, do my distance healings, do energy work exercises and overall just get away from everything else. There have been a few instances which stand out even more to me. Almost every time I go to the beach, it is actively being sprayed with the only exception in recent memory being a 2 week reprieve after hurricane Ivan tore through to Texas. It was blatantly noticeable to me because the sky looked so healthy for 2 weeks and all the clouds looked vibrant and natural. One very noticeable instance I was at the beach with my sister and when I arrived there was a huge area of the sky that was blanketed with very noticeable fake clouds. It stood there for 2 hours and did not move or dissipate at all prior to me doing some work on it. I opened up my peripheral vision to the cloud structure, said the prayer out loud 4 times with intent and allowed myself to drop into a dreamy alpha like state. Over the next 20 minutes I watched this large ugly wispy cloud system begin to move in on itself, bunch up into several squares which became several smaller squares which eventually dissipated and ended up 10% of its original size and looked like beautiful ordinary clouds with zero resemblance of the ugly mist like structure they had before. I had another incidence of this exact occurrence and pattern, cloud system drawing into itself and becoming several squares, happen about a month after the first one.
Other methods I have worked with while at the beach I used against entire storm fronts which more or less stopped in their tracks. Huge ugly storm fronts came in over the beach (more than once), I raised my energy vibration to where I felt the clouds and their presence and I told them not to rain on my parade. Not a single drop of rain on me for hours at the beach alone more or less by myself with a 70% chance of rain for the day. The storm system eventually made its way over my head after creeping slowly in off the Ocean, much slower than its original trajectory, at which point I actually started connecting with the sun and pulling its rays through the clouds. The cloud system would become splotchy, lose its density and the sun would start creeping through. I ended up getting sun for 3 out of the 4.5 hours I was at the beach with a storm system directly over head. The other hour and half the storm just sat there and eventually ended up dissipating over the area.
I've worked with Tachyon energy beams that I created through intent that likewise have cleaved sections out of clouds. I am energy perceptive and can see the energy when I work with it. In the future I plan to experiment with constructing Etheric Orgone arrays like mentioned by Grey Wolf in his healing thought forms article. I have no doubt that they will work as a large amount of my healings I do on people I do in the Etheric plane outside of my body working on other peoples energy bodies. Also when I build thought forms and etheric objects, I can perceive them energetically. I have a large thought form I put on top of a building across the street from my office. The top of this building has 'Cell Phone' radars that look identical to the fake cell tower arrays you have posted on your page; this thought form transmutes any negative energy flowing through them into a beneficial energy. Whatever group operates them will be in for a surprise once they turn them on and none of the electromagnetic pulse reaches their targets and whatever base they work from suddenly gets cleared of all their negative energy pathways. I can actually see this large thought form when I look out my window at this building. It, in and of itself, is self sustaining and based around an Orgone matrix. Every now and again I check on the various thought forms I have created and any of them I have put in place with permanence has not only remained in place but I have found them to become stronger in their application. I leave all Etheric creations open to use and optimization of higher energy spirits which work within the light and work for the greatest good of humanity.
2. Then before I breathe in again, I make a strong directive like "remove these chemtrails from the skies NOW!" (the energy which I emitted which is intelligent is just waiting for a command.) I couple it with looking right at the middle of the HAARP cloud and imagining a blue hole expanding from it like what Drew was imagining. I always finish the directive with NOW so it knows that it must do it in the present time. Sometimes it happens immediately, sometimes later, but it does happen most of the time.
3. I repeat this for a total of 4 times. then I finish with 4 more "mahalo" breathing, which means thank you in Hawaiian. I notice that when I finish with mahalo, the results are much more spectacular than when I don't use it. In fact, I feel the most tingling in my hands when I express gratitude.
4. I believe that you can use any indigenous power word that resonates with you that has the same "aoa" or "aua" or "aaa" vowel configuration because I believe that these words have been hidden in every culture. this includes "yehovah", "yeshua", "ahava", "talofa", "mabuhay" etc. usually this word will mean God, love, to live, life energy etc in that language.
Since I've been doing this, I have: had lost keys materialize in my back pocket which I checked thoroughly first; turned a lifelong, very defensive, offensive, paranoid relative into a loving more open person (I mean total change like a switch was flipped). I had a wave hog standup surfer move to another location, brought in more business for my company, avoided a potential mishap on my motorcycle, avoided ripping my eye out on the reef while surfing etc.
There's many more big and little things that I do with this. That it happens so naturally, I just forget about it now. It's like manipulating reality is a natural occurence just like what the ancient Hawaiians believed. To them, there was no such thing as "supernatural" and "sacred". Everything was natural and sacred and weird happenings and synchronicities were part of daily life. And no, this just doesn't happen in Hawai'i where the fabric of reality is a lot thinner; I've done this on our travels all over Asia.
I hope more people do realize this and hopefully if they use this technique, they can tell you if it worked for them.


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Quantum Break Developer Says Game Awards Trailer Will Be 'Best Footage Yet'
The trailer is said to be very different and fresh.
Posted By Oliver VanDervoort | On 30th, Nov. 2015
We've been hearing quite a bit about the graphics quality of Quantum Break basically since the game was first announced. The company doubled down on what it thinks are going to be truly impressive graphics. Now Remedy Entertainment has announced that they are going to be showing off even more in a new trailer that will air at this week's Video Games Awards show. Remedy says the new trailer is going to be bringing new and fresh content that will also be quite good looking.
On the official Remedy Twitter account, the firm also said this will be the best footage yet. There were a couple of other announcements that followed that tweet, with Microsoft announcing on its own Twitter account that Quantum Break won't be the only Xbox One game scheduled to be featured on the Video Game Awards show.
Aaron Greenberg, the Xbox games lead marketer would not go into details but did say there were going to be other games that will make an appearance on the show. Quantum Break looks like it's going to be getting quite a bit of the focus though, especially considering Remedy is talking about being in the home stretch of the development process. Sam Lake himself said the company is making its final push in order to get the game done on schedule. Quantum Break is scheduled for launch exclusively on the Xbox One on April 5, 2016 and apparently if you watch the Video Games Award show this Thursday you'll be able to get another peek at the game.
Tagged With: Microsoft, Quantum Break, remedy entertainment, Xbox One
Developer:Remedy Entertainment
Platforms:Xbox One, PC


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Town of Seabrook Island Issues Third Public Advisory on COVID-19 (Coronavirus)
At 3:00 pm on Friday, March 13, 2020, President Donald Trump declared a National Emergency over the Coronavirus 2019 (COVID-19) pandemic and announced a set of specific measures aimed at stemming the effects of the outbreak. The declaration frees up approximately $50 billion in federal funds under the Stafford Act to fight the fast-spreading virus. The declaration grants broad authority to the Secretary for Health and Human Services to waive provisions of certain laws and regulations to give doctors and hospitals maximum flexibility to respond to the virus and requires every state to open emergency operation centers. President Trump also announced that he was waiving interest on all student loans held by federal government agencies and has directed the Secretary of Energy to purchase large quantities of crude oil for the US strategic reserves to take advantage of low oil prices.
At 5:00 pm on Friday, March 13, 2020, Governor Henry McMaster declared a State of Emergency to enhance the state's response to the COVID-19 virus. The Governor's emergency declaration includes:
Immediate restriction on visitation to nursing homes and assisted living facilities throughout the state (with the exception of end of life situations);
Immediate suspension of visitation at state and local correctional facilities in all 46 counties;
Immediate activation of the state's price gouging laws;
Immediate activation of the State Emergency Management Plan;
Closing of all schools in Kershaw and Lancaster Counties for a period of 14 days;
Directing the SC Department of Health and Environmental Control (SCDHEC) to consult with the state's Superintendent of Education and local school district leadership to provide guidance on if and when remaining school districts should close schools and for what period of time; and
Confirming that state government offices shall remain open during their normal business hours.
At this time, the Town of Seabrook Island and Charleston County government remain under normal operating conditions.
For general questions about COVID-19, please contact the SCDHEC Care Line at (855) 472-3432. Staff will be available to answer calls from 8:00 am to 6:00 pm seven days a week.
For the most reliable information about COVID-19, residents are strongly encouraged to visit official resources, including the SCDHEC and CDC websites.
Presidential Proclamation on Declaring a National Emergency Concerning the Novel Coronavirus Disease (COVID-19) Outbreak
Governor Henry McMaster's State of Emergency Declaration


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Obituary: Chester William Fannon III
Chester William Fannon III (Chet) of Middleburg, Va. died peacefully on Saturday, Dec. 3, 2016 with his wife, Kate Armfield Fannon and his sister, Heather Fannon Young by his side.
A loving husband to Kate and a respected and cherished father to Kingsley and Chester, Chet was born on Oct. 21, 1961 in Alexandria to Chester William Fannon Jr. (Bill) and Mary Frances Tucker Fannon. His childhood was spent at Laurel Hill in Rappahannock County, Va. His love of and years spent on the family farm fostered his lifelong passion for the outdoors, bird hunting, dog training and habitat restoration. He also enjoyed horseback riding and had been an accomplished polo player.
Chet was a graduate of the Blue Ridge School in Albemarle County and James Madison University in Harrisonburg and enjoyed a career with Fannon Petroleum.
In death, Chet showed the same courage, integrity and grace that had been the hallmarks of his life. He is remembered with love and missed with heartache by his wife Kate, his daughter Kingsley and son Chester; parents Bill and Mary Frances Fannon; sisters and their husbands, Beth and Jimmy Swindler and Heather and Daron Young; nieces Addie Swindler, Ellie Young, and Claire Young; and nephew Trey Swindler; and beloved in-laws, Howard and Gloria Armfield.
A memorial service will be held on Thursday, Dec. 8 at 11 a.m. at Trinity Episcopal Church in Upperville, Va. Family and friends are invited to gather for remembrances at the Middleburg Tennis Club after the funeral service. In lieu of flowers, donations can be made in Chet's memory to the United Network for Organ Sharing (UNOS) at 700 N. 4th Street, Richmond, VA 23219 or at www.unos.org.


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Cross-Border Activity Slows Overall, But Domestic IPO Markets Buck Downward Trend
Overvaluations and geopolitical concerns see cross-border market decline overall
Global exchanges jockeying for position in competitive environment for listings
November Alibaba listing in Hong Kong and Saudi Aramco's IPO on the Tadawul improves an otherwise sluggish year for capital raising
Total IPO activity globally fell by 20% to 1,242 and capital raised fell 8% to USD 206.1 billion. Domestic IPO activity generally bucked the overall downward trend with total capital raised up by 4% to USD 167.4 billion, although the total number of domestic IPOs dropped by 20% to 1,048. Both the US and China saw strong domestic activity with several marquee deals. Geopolitical uncertainties, particularly in major financial markets, such as the US, UK and Hong Kong, dampened IPO activity and left investors waiting on the sidelines, hoping for resolution to trade disputes and political uncertainty.
Koen Vanhaerents, Baker McKenzie's Head of Global Capital Markets, says:
"It has been an interesting year for the global capital markets as unexpected issues, both in the market and politically, have significantly impacted upon activity and investor sentiment. While we entered 2019 on an optimistic note, underperformance of a number of larger listings coupled with heightened political issues saw a more muted end to the year than anticipated. Despite these macro-environment factors, we saw some of the largest IPOs of all time, with issuers braving the elements to go public and raise capital ahead of what is expected to be a downturn in the global markets in 2020."
These and other findings are published today in the Cross-Border IPO Index 2019.
Cross-Border IPO Activity Slows
2019 overall has been a year of uncertainty in many jurisdictions. Cross-border deal value dropped by 35% year over year to USD 41 billion, while volume dropped by 17% to 197 deals. The Alibaba listing saw Retail claim the top spot for capital raising by industry, without which Financials would have retained the title – instead coming in second and followed by Healthcare and Consumer Products and Services. Financials did claim top place for value overall, followed by High Technology, Energy and Power, and Retail.
Many listings were delayed or cancelled with most citing poor investor demand and low pricing as the biggest factors in their deferrals. Some of the largest cancelled listings this year included GFL Environmental (which had hoped to raise over USD 2 billion), Homeplus K-REIT, ReAssure, Latitude Financial, Endeavor, Virgin Trains USA and Vine Resources.
One notable listing that was rumoured to list earlier in the year but potentially delayed by political unrest or price volatility in Hong Kong until late November, was Alibaba, which listed on November 25, raising USD 11.2 billion. Two other large listings, Budweiser's (USD 5 billion) and ESR's (USD 1.6 billion) listings, which were aborted earlier in the year, also relaunched and listed in the fourth quarter. Even without the Alibaba listing, Hong Kong was the leading destination for cross-border IPOs, both in terms of value and volume, but the listing was a shot in the arm for the Hong Kong exchange, where overall value and volume is down significantly from 2018, with a drop of 7% in value and 28% in volume.
Nasdaq was in second position behind Hong Kong for the leading cross-border IPO destination with USD 5.4 billion raised from 51 IPOs.
EMEA saw a 71% drop in cross-border IPO activity with just 10 IPOs raising USD 4.7 billion.
The Cross-Border IPO Index 2019 is down by 18% to 19.5, reflecting the major decline in the number of listings and amount raised outside issuers' home jurisdictions.
In the US, domestic IPO deal value moved to USD 58.1 billion in 2019 from USD 44.3 billion in 2018, a 31% increase that was driven largely by a number of high-value deals. In fact, all mega IPOs – raising over USD 1 billion – were domestic, and led by Uber's USD 8.1 billion offering. Several of these deals had been in the pipeline for some time, and some observers noted that many came to market in 2019 to take advantage of favorable conditions that could change due to the US presidential election in 2020.
Despite the positive movement domestically, the big story in the US was the overvaluation of a number of pre-profit tech unicorns, whose subdued performance post-IPO led to investors to look cautiously at similar listings. This effect was most notable with the fall of WeWork's highly anticipated offering – which added weight to the question of whether the private market valuations are a good indicator of strong IPO performance.
The Cross-Border IPO Index 2019 score for North America has fallen by 29% to 20.2, which is close to the global weighted average of 19.5 for 2019.
Christopher Bartoli, Baker McKenzie's Head of North America Capital Markets, says:
"We started the year with high expectations for a number of planned tech unicorn IPOs with possible record valuations. While a number of these unicorns completed their IPOs, several have seen significant price declines due to investor concern with their business models or path and timing to future profitability. As a result, we have seen a number of companies delay their IPOs in order to streamline and focus their operations, reduce costs and attempt to forge a path to profitability.
"Despite this, domestic capital raising in North America hit its highest level since 2014 and we expect to see the region continue to buck the global trend well into Q1 2020 as issuers look to list ahead of the 2020 elections."
In Asia Pacific, IPO activity has fallen significantly in 2019 compared to 2018's stellar performance, which was mostly driven by an uptick in high-value Chinese cross-border deals into Hong Kong. Both the amount of capital raised and the number of IPOs overall fell to USD 90.4 billion from 776 listings, a drop from USD 109 billion and 927 listings in 2018.
Chinese issuers led the way with 260 IPOs, 179 of which were domestic, followed by South Korea with 92 IPOs, all domestic; Japan with 90 IPOs, 89 of which were domestic; and India with 63 IPOs, all domestic. Financials was the leading sector, raising USD 16.3 billion. In addition, capital raised by High Technology increased by 12% over 2018 and Retail showed a 64% increase in capital raising year-on-year, due to the Alibaba offering.
There were a number of examples in Asia Pacific of new approaches from exchanges to lure companies to list in the region. For example, China launched the Science and Technology Innovation Board or STAR market, which was designed to encourage domestic tech companies in particular, to list locally. There were 47 listings on STAR in 2019, raising over USD 9.5 billion, as the exchange got off to a strong start. It is worth noting that not only did the number of Chinese IPOs into the US decline, domestic tech listings showed an increase of 19%.
In addition, June saw the launch of the London/Shanghai Connect – a stock exchange trading link that permits global investors to access shares in Chinese companies and Chinese investors to buy stock on the LSE. This was seen as a boon for both markets and a particularly innovative policy change from China, who have been making radical changes to attract more offerings to its equity markets.
The November Alibaba "homecoming" listing in Hong Kong (after Xiaomi and Meituan) is a showcase of attraction that the Hong Kong Stock Exchange is able to get from unicorns, since its regulatory changes in April 2018 to encourage innovative and biotech company listings.
The Asia Pacific Cross-Border IPO Index 2019 fell by 7% to 24.5.
Ivy Wong, Baker McKenzie's Head of Asia Pacific Capital Markets, says:
"Uncertainty will always influence the markets, with few major financial centers escaping unscathed this year. While the disturbances in Hong Kong did hamper activity to a degree, performance remained relatively stable – as the infrastructure and investor base was still reliably there for issuers. Alibaba is a good example of this.
Going forward, we are set to see the 'battle of the exchanges' heat up, with recent regulation changes throughout the wider Asia Pacific region, coupled with the launch of the STAR market already luring listings away from, or at least providing issuers with more options in addition to, traditional venues such as Nasdaq and NYSE."
Although the Saudi Aramco IPO is set to boost capital raising in EMEA, Brexit and weak economic activity across the Eurozone resulted in a slow IPO market overall.
Volume dropped by 46% to 113 IPOs and value remained static at USD 45.6 billion, helped by the 10 mega IPOs in the region. Most of the listings were domestic, leading the Cross-Border IPO Index to fall 36% to 10.8, the lowest of all the regions.
While the Aramco listing made up 50% of domestic capital raising, there were eight other domestic mega deals in the region – with London and Frankfurt proving popular for larger listings, and Saudi Arabia's Tadawul seeing the first truly international offering with Arabian Centre's Rule 144A IPO. Italy's stock exchange was another bright spot in an otherwise muted landscape, with a 50% increase in IPOs.
The low number of cross-border listings hit the region hard with activity 71% lower than 2018.
Adam Farlow, Baker McKenzie's Head of EMEA Capital Markets, says:
"While Brexit continued to pummel cross-border activity in the region, there were pockets of success among domestic activity – with a number of exchanges including London, Riyadh, Frankfurt and Italy playing host to billion dollar listings.
"We are finally set to see the debut offering from Aramco, which is expected to rocket the Tadawul to the top of the board. It's been a real rollercoaster for the EMEA markets of late, but we can expect to see big things in 2021, as ongoing political and economic issues are finally put to bed, releasing pent-up demand."
Widespread political unrest in the region dampened IPO markets in both value and volume. A total of USD 3.5 billion was raised during 2019, down 33% from 2018, and deal volume fell by 30% to seven. All listings were domestic with Brazil and Chile seeing all of the activity in the region.
There were five IPOs in Brazil, an increase from three in 2018 - said to be driven by the pension reforms that were passed by Brazil's senate in October. In fact, two of these offerings were listed the very day the pension reforms were passed. In Chile, there was increased activity in the first half of the year followed by a slowdown due to political and civil unrest in the second half of the year.
Pablo Berckholtz, Baker McKenzie's Head of Latin America Capital Markets, says:
"Despite the decline in numbers and heightened economic and political events affecting much of the region, countries such as Brazil, Colombia and Peru are holding their own at a macro level – with companies that continue to perform well, undeterred by market issues.
"Overall, there has been a notable improvement in the way business is being conducted over the past few years – which we can expect to have a positive impact on future economic growth."
Stock Exchanges up their Game
Even with more listing venue options than ever for issuers, the US and China remain the strongest players with Hong Kong, Nasdaq and the NYSE leading in capital raising globally. Nasdaq was the most active exchange in 2019 with 183 issues. The Alibaba listing was responsible for Hong Kong's retention at the top of the board for value.
Shanghai's STAR Market boosted China's performance, raising over USD 9.5 billion, which accounted for around 30% of the capital raised in China in 2019, and potentially accounting for the decline in Chinese issuers in the US and the increase of Chinese domestic IPOs.
Although London is still a top five cross-border listing destination, following a number of delayed deals it only saw four cross-border listings in 2019, down from 16 in 2018. Australia increased its cross-border capital raising by 432%, largely due to the USD 631 million SPAC IPO from KKR Credit Income Fund. Bright spots included domestic activity in Italy with increases in IPO value and volume, as the quantitative easing by the European Central Bank made an impact, coupled with a change in leadership in September, as well as the growth in activity in Saudi Arabia's Tadawul.
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Leah Schloss
Associate Director, Communications, North America
+1 212 626 4474 Email
Cross-Border IPO Index 2019: Global IPO Market Contracts Under Political Uncertainty
Koen V. Vanhaerents
Christopher M. Bartoli
Pablo Berckholtz
Adam B. Farlow
Ben McLaughlin
Ivy Wong


Total shoulder arthroplasty (TSA) is becoming increasingly more common as a treatment for disabling pain or impaired shoulder function. Dr. Jonelle Petscavage, a Medical Metrics' (MMI) consultant, recently published a two-part review in the American Journal of Roentgenology on the current state-of-the-art in shoulder arthroplasty. Covering topics such as epidemiology, history, preoperative imaging, hemiarthroplasty, anatomic and reverse TSA, and non-prosthetic resurfacing, Dr. Petscavage represents the level of expertise that sponsors can expect from collaborating with MMI on their regulated and non-regulated orthopedic studies.
MMI has been able to leverage this expertise in the support of several new stemless shoulder arthroplasties. The stemless humeral component design represents a novel approach to reducing the complication rate found in traditionally-designed TSAs.


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Fine Panama, Sambu Choco Indian Wood Carving from Chief Provenance Collection 40
The provenance that accompanies this collection is wonderful coming from the personal collection of Dr. Peterson who graduated from Hillsdale College & University of Michigan Medical School in 1943 and served in the Navy in the final days of WWII and later in Korea. Carl and his wife moved to the Panama Canal Zone to practice medicine for 10 years during the 1970's of which he personally acquired all works. He became incredibly close with different aboriginal people groups whom they gifted many carvings. Not only did he have a personal fascination with carvings but also had a significantly large collection of Pre-Columbian pottery. Carl traveled and collected the majority of carved aboriginal works from.
Sambu River, Panama, Choco Peoples. San Blas Islands, Kuna Peoples.
He also participated in many excavations uncovering many Pre-Columbian pottery examples from. Graves of Sitio Conte, Cocle Province.
Carl kept a hand written journal documenting when and where each piece was acquired indicated by a combination of letters (identifying the place of origin) and a number (indicating the number piece from that particular region) seen either written on the bottom of each object or on a taped label. The people groups loved him so much he even has indicated that Chiefs had personally given him their personal items of affection. Carls also became close friends with Eva Harte whom he traded pieces back and forth with. Up for sale is the most rare and fine wood carving I currently have available showing a large double authority stick from the Sambu Choco Indians of Panama's Darien forest.
What makes this such a special example is that is was given by the Sambu village Chief Jauleto to Carl as a gift. Measuring 25 inches tall the work is in excellent original condition with the reference number "SA-32" as seen written on its paper label (faded) which is recorded as "Large Double Authority Stick - 2 Males Back to Back on an Elephants back made by Jualeto, Chief of the Sambu Village - a Gift" in Carl's recorded notebook of acquisitions. Please take note the different arm position each figure shows, one with hands down to his sides while the other crosses them over his chest. This is a tremendously rare and unique indigenous wood carving from the Indian chief himself! The images provided accurately represent the quality, condition and aesthetic beauty of this fine carving but if you have any questions please feel free to ask prior to purchasing! All available works would make an exceptional addition to anyones collection from rare small people groups who make fascinatingly beautiful work. We specialize in fine art from the Renaissance to Contemporary dealing with a plethora of past artists which include Pablo Picasso, Diego Giacometti, Edward Curtis, Alfred Mitchell, Banksy and even Bob Ross.
All works of art and objects of value are professionally packed to ensure a safe arrival to you, thank you for your interest! This item is in the category "Art\Art Sculptures".
The seller is "henningfineart" and is located in this country: US. This item can be shipped to United States, Canada, United Kingdom, Mexico, Germany, Japan, France, Australia, Denmark, Romania, Slovakia, Bulgaria, Czech Republic, Finland, Hungary, Latvia, Lithuania, Malta, Estonia, Greece, Portugal, Cyprus, Slovenia, Sweden, Korea, South, Indonesia, Taiwan, South Africa, Thailand, Belgium, Hong Kong, Ireland, Netherlands, Poland, Spain, Italy, Austria, Bahamas, Israel, New Zealand, Singapore, Norway, Saudi Arabia, Ukraine, United Arab Emirates, Qatar, Kuwait, Bahrain, Croatia, Republic of, Malaysia, Chile, Colombia, Costa Rica, Panama, Trinidad and Tobago, Guatemala, Honduras, Jamaica, Barbados, Bangladesh, Bermuda, Brunei Darussalam, Bolivia, Ecuador, Egypt, French Guiana, Guernsey, Gibraltar, Guadeloupe, Iceland, Jersey, Jordan, Cambodia, Cayman Islands, Liechtenstein, Sri Lanka, Luxembourg, Monaco, Macau, Martinique, Maldives, Nicaragua, Oman, Peru, Pakistan, Paraguay, Reunion, Vietnam, Uruguay.
Provenance: Ownership History Available
Region of Origin: Panama
Type: Carving
Style: Folk & Indigenous


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Rebecca is a Toronto based Director, Editor and Producer interested in the intersection of independent filmmaking and the storytelling applications of digital video production and dissemination technology. She holds and BFA and MFA in film production from York University.
Her directorial work has screened at The Montreal World Wide Film Festival, The Moving Images Festival, The International Student Film Festival Hollywood and Toronto's Female Eye Film Festival (where her film Birdbath was nominated for Best Short Film).
Rebecca is skilled at narrative, documentary and commercial editing and has over six years experience editing broadcast, web and festival content. She has worked with Directors Lesley Johnson, Scott Miller Berry, Mark Pariselli, Matthew Hogue, Jennifer Dysart and Francis Lebouthillier. These collaborations were showcased internationally in festivals including Oberhausen, Experimenta, Rotterdam, Inside Out, Imaginative and Nuit Blanche. Her freelance clients include Toronto International Film Festival, Cream Productions, The Royal Ontario Museum and Idea Couture.
She learned how to produce by producing her own films and has since worked as a Producer, Assistant Director, Production Coordinator and Production Manager on independent feature films and for companies like Cream Productions and Vice Media.
GRUIHN //