text:
\section{Introduction}
\label{sec:intro}
It is now widely accepted that a large class of extremal and
near-extremal black holes can be described in string theory.
The evidence for this correspondence falls in two broad categories:
first, the counting of string states agrees with the degeneracies
inferred from the Bekenstein-Hawking area
law~\cite{sv1,callan96a} (also~\cite{sen95,structure,ct2});
and second, the rate and spectrum of Hawking radiation agrees in the two
descriptions~\cite{callan96a,mathur,greybody}. The string theory
side of the counting involves two distinct contributions to the
entropy, from the right and left moving excitations of the string;
and similarly the emission spectrum of the string is characterized by
two independent temperatures, because the initial state has quanta
in both sectors. The agreement requires that the classical geometry
reproduces these duplications of thermodynamic variables; and this is
indeed the case, at least in the so-called dilute gas regime.

The appearance of two independent sets of thermodynamic variables is
related to the presence of two event horizons. For example the two
contributions to the entropy are proportional to the sum and
difference of the inner and outer horizon area, respectively. This
geometric interpretion of the thermodynamic variables gives access to
properties
of the underlying microscopic theory that seems to be valid for
{\it all} black holes. In a previous paper we explained  these
results for the most general black holes in five dimensions~\cite{cl97a}
(see also~\cite{cveticreview,fl97}). The purpose of the present paper
is to present the corresponding calculations for a large class of
rotating black holes in four dimensions. Our focus will be on the differences
between the two cases; so a number of interpretive remarks will not
be repeated.

The description of black holes in string theory is
more involved in four dimensions than in five dimensions.
In particular, the effective string models for the entropy are less
rigorous~\cite{structure,strom96d,crr,kt,vf}; and the microscopic
foundation of the proposed exact BPS-degeneracy~\cite{dvv3}
is less clear than the analogous one in five dimensions~\cite{sv1}.
The regime of agreement between the emission spectrum of
the string model and the Hawking radiation of semiclassical description
is also more restrictive in four
dimensions~\cite{klebanov96b,mathur97,strominger97a}.

The interpretation of greybody factors is simplest in the regime where
the radiation is the result of a two-body process in the underlying
string theory. In~\cite{cl97a} we found that for five dimensional black
holes the rotational parameters can be tuned so that greybody factors
retain their characteristic two-body form, without restrictions on
the charges. Here we will find no comparable simplifications in four
dimensions. Despite this limitation many cases remain where the
radiation can be described as the result of a two-body process. An
important example is the low energy limit of the radiation from the
most general black holes.

New possibilities arise if we also consider multi-body processes
in the effective string theory. It is particularly interesting to
consider processes with higher partial wave number.
In both four and five dimensions the partial wave number can be chosen
so that these processes can be described analytically in the
classical theory for general non-extremal black holes, and even at high
energy. The structure of the resulting emission rates has a characteristic
multi-body form that can be interpreted in an effective string theory.

The paper is organized as follows. In sec.~\ref{sec:waveeq},
we present the wave equation for a minimally coupled scalar field in
the background of a rotating black hole in four dimensions.
We interpret the various terms. In sec.~\ref{sec:solution}, we
solve the equation in various regions, and match these exact solutions
to find approximate wave functions that are valid throughout. This leads
to a general expression for the absorption cross-section. In
sec.~\ref{sec:examples} the region of applicability of this result is
determined, and we present examples. In sec.~\ref{sec:discussion} we
discuss the microscopic interpretation of our classical calculations
in terms of an effective string theory with emphasis on applications
to general non-extremal black holes.

\section{The Wave Equation}
\label{sec:waveeq}
We consider a class of four-dimensional rotating black hole in
toroidally compactified string theory. It is parametrized by the mass $M$,
angular momentum $J$, and four independent $U(1)$ charges
$Q_i$~\footnote{The most general black hole in four dimensions is
parametrized by five charges~\cite{ct2,hull96}. It has not yet been
constructed.}. This black hole solution was given explicitly
in~\cite{cy96b}; and
its non-rotating form appeared in~\cite{cystrings,hlm}. In special
cases the black hole reduces to a solution of Einstein-Maxwell
gravity. For example the Kerr-Newman black hole corresponds to all
four charges equal.

It is often convenient to parametrize the physical variables $M$,$Q_i$,
and $J$ in terms of auxiliary quantities $\mu$,$\delta_i$, and $l$
defined as:
\bea
M &=& {1\over 2}\mu\sum_{i=1}^4 \cosh 2\delta_i~, \\
Q_i &=& {1\over 2}\mu \sinh 2\delta_i~~;~~~i=1,2,3,4~, \\
J &=& {1\over 2}\mu l~(\prod_{i=1}^4 \cosh\delta_i -
\prod_{i=1}^4 \sinh\delta_i)~.
\label{eq:l12def}
\eea
The gravitational coupling constant in four dimensions
is $G_4={1\over 8}$. In string units this corresponds to
$(2\pi)^6(\alpha^\prime)^4/V_6$.\footnote{The $m$ of~\cite{cy96b}
is $m={1\over 4}\mu$ and also $l_{\rm there}={1\over 4}l_{\rm here}$.
The $r_0$ of~\cite{hlm} is $r_0={1\over 2}\mu$.}
With these conventions the areas $A_{\pm}$ of the inner and outer event
horizons imply the entropies:
\bea
S_{\pm} &\equiv& {A_{\pm}\over 4G_N}=
2\pi[
{1\over 2}\mu^2 (\prod_i \cosh\delta_i+\prod_i \sinh\delta_i)
\pm
\sqrt{{1\over 4}\mu^4 (\prod_i \cosh\delta_i-\prod_i \sinh\delta_i)^2-J^2}]
\nonumber \\
&=&2\pi [
{1\over 2}\mu^2 (\prod_i \cosh\delta_i+\prod_i \sinh\delta_i)
\pm
{1\over 2}\mu\sqrt{\mu^2-l^2}(\prod_i \cosh\delta_i-\prod_i \sinh\delta_i)]~.
\label{eq:ent4d}
\eea
In the string theory interpretation the two terms:
\bea
S_L &=& \pi\mu^2 (\prod_i \cosh\delta_i+\prod_i \sinh\delta_i), \\
S_R &=& {1\over 2}\mu\sqrt{\mu^2-l^2}
(\prod_i \cosh\delta_i-\prod_i \sinh\delta_i),
\eea
are the entropies of the left (L) and right (R) moving excitations.

We consider a minimally coupled scalar field propagating in the background
of the black hole. The wave equation is the Klein-Gordon equation:
\be
{1\over\sqrt{-g}}\partial_\mu (\sqrt{-g}g^{\mu\nu}\partial_\nu \Phi) =0~.
\ee
It is convenient to introduce the dimensionless radial coordinate:
\be
x \equiv {r - {1\over 2}(r_{+}+r_{-})\over r_{+}-r_{-}}~,
\label{eq:xdef}
\ee
so that the outer and inner event horizons are located at
$x=\pm {1\over 2}$, respectively; and the asymptotic
space is at large $x$. The wave function is written in spherical
coordinates as:
\be
\Phi\equiv\Phi_r(r)~\chi(\theta)
e^{-i\omega t+im\phi}~.
\ee
Then the radial part of the wave equation becomes:
\bea
&~&{\partial\over\partial x}(x^2-{1\over 4}){\partial\over\partial x}\Phi_r
+{1\over 4}[ x^2\Delta^2\omega^2 +
xM\Delta\omega^2-4{\tilde\Lambda} \label{eq:geneq}
\\
&+&{1\over x-{1\over 2}}
({\omega\over\kappa_{+}}-m {\Omega\over\kappa_{+}})^2
-{1\over x+{1\over 2}}({\omega\over\kappa_{-}}-
m {\Omega\over\kappa_{+}})^2]\Phi_r = 0~. \nonumber
\eea
This equation is our main technical result\footnote{The main intermediate
step is to calculate the determinant of the metric. It turns
out that the result is simple: $-g=\Delta\sin^2\theta$, in the
notation of~\cite{cy96b}.}. It is not more complicated than
special cases that
have been considered previously~\cite{klebanov96,mathur97,strominger97a},
but the present context is more general. In the following we
explain the notation and interpret the various terms.

The variable $\Delta$ is defined as:
\be
\Delta = 2(r_{+} - r_{-}) = \sqrt{\mu^2 - l^2} = \beta_H^{-1}S~.
\label{eq:deltadef}
\ee
($T_H=\beta^{-1}_H$ is the Hawking temperature.)
The first equation, and the definition of the radial variable $x$,
ensures that the wave equation reduces at large $x$ to the Klein-Gordon
equation in {\it flat} space, as it should. Accordingly the term
${1\over 4}x^2 \Delta^2\omega^2$, dominant at large $x$, can be
interpreted as the energy of the scalar field at infinity.

At large $x$ the mass-term ${1\over 4}xM\Delta\omega^2$ is suppressed
relative to the energy of the scalar field at infinity
by one power of $x\propto r$, as expected for a long
range Coulomb type interaction in four dimensions.

The effective angular momentum barrier $\tilde{\Lambda}$ is the term
that is suppressed by $x^2\propto r^2$ for large $x$. It is:
\be
{\tilde\Lambda} = \Lambda - {1\over 16}\mu^2\omega^2 (1 + \sum_{i<j}
\cosh 2\delta_i \cosh 2\delta_j)~,
\ee
where $\Lambda$ is the eigenvalue of the operator:
\be
{\hat \Lambda} = -{1\over\sin\theta}{\partial\over\partial\theta}\sin\theta
{\partial\over\partial\theta} - {1\over\sin^2\theta}
{\partial\over\partial\phi^2}-{1\over 16}l^2 \omega^2 \cos^2\theta~,
\label{eq:anglap}
\ee
which is simply the angular Laplacian in four flat dimensions, except
for the last term which reflects the rotation of the black hole background.

The terms that are most important for the microscopic interpretation
are the horizon terms at $x=\pm {1\over 2}$.
Their form is such that $\kappa_{\pm}$
are the physical surface accelerations at the inner and outer
horizons~\cite{cl97a}. They are given by:
\bea
{1\over\kappa_{\pm}}
&=&
{{1\over 4}\mu^3 (\prod_i \cosh^2\delta_i-\prod_i \sinh^2\delta_i)\over
\sqrt{{1\over 4}\mu^4 (\prod_i \cosh\delta_i-\prod_i \sinh\delta_i)^2-J^2}}
\pm
{1\over 2}\mu (\prod_i \cosh\delta_i-\prod_i \sinh\delta_i)
\nonumber \\
&=&
{\mu^2\over 2\sqrt{\mu^2-l^2}}
(\prod_i \cosh\delta_i+\prod_i \sinh\delta_i)
\pm
{1\over 2}\mu (\prod_i \cosh\delta_i-\prod_i \sinh\delta_i)~.
\eea
Similarly, $\Omega$ is the angular velocity at the outer event horizon,
given by\footnote{The angular velocity at the inner event horizon
is given through
${1\over\kappa_{-}}\Omega_{-}={1\over\kappa_{+}}\Omega$. The appearance
of $\kappa_{+}$ in the inner horizon term is due to the convention that
$\Omega$ is measured at the outer horizon.}:
\be
{1\over\kappa_{+}}\Omega ={J\over
\sqrt{{1\over 4}\mu^4 (\prod_i \cosh\delta_i-\prod_i \sinh\delta_i)^2-J^2}}
= {l\over\sqrt{\mu^2-l^2}}~.
\ee
These expressions for $\kappa_{\pm}$ and $\Omega$ agree with those
that follow from the entropy (eq.~\ref{eq:ent4d}), by use of thermodynamic
relations.

\section{Calculation of Absorption Cross-section}
\label{sec:solution}
The wave equation cannot in general be solved exactly. However we can
find solutions valid in the asymptotic region and match them with
solutions valid in the horizon region to find approximate wave functions
that apply throughout spacetime. The calculations follow previous
work closely~\cite{greybody,mathur97,strominger97a,dowker,hawking97}.

\paragraph{The angular equation:}
Consider first the angular Laplacian
$\hat{\Lambda}$ (eq.~\ref{eq:anglap}). The eigenfunctions are the
spheroidal functions (see {\it eg}.~\cite{abramowitz}):
\be
\chi(\theta)=S_{mn}({l\omega\over 4},\cos\theta)~.
\ee
The corresponding eigenvalues $\Lambda$ are labelled by the orbital
angular momentum $n$ and the azimuthal quantum number $m$. They can be
represented by a power series in $({l\omega\over 4})^2$ as:
\be
\Lambda (n,m) = n(n+1) + {1\over 2}
[1 - {(2m-1)(2m+1)\over (2n-1)(2n+3)}]({l\omega\over 4})^2+\cdots
\ee

\paragraph{The asymptotic region:}
Next consider the radial equation. At large $x\gg 1$ we omit the
horizon terms so that the radial wave
equation becomes:
\be
{\partial\over\partial x}x^2{\partial\over\partial x}\Phi_\infty
+{1\over 4}[x^2\Delta^2\omega^2+xM\Delta \omega^2-
4{\tilde\Lambda}]\Phi_\infty
= 0~.
\ee
Denoting the solutions in this region $\Phi_\infty^{\pm}$ we find:
\be
\Phi_\infty^{\pm} = x^{-{1\over 2}\pm \zeta}
e^{-{i\over 2}\Delta\omega x} C_{\pm}
M_K({1\over 2}\pm\zeta-{i\over 4}M\omega,1\pm 2\zeta,i\Delta\omega x)~,
\label{eq:infwavefct}
\ee
where the function $M_K$ is Kummers function (see e.g.~\cite{abramowitz}),
the parameter $\zeta$ is\footnote{The parameter $\xi$ of~\cite{cl97a}
can be introduced as $\xi={1\over 2}+\zeta$. The present notation gives
more symmetric formulae.}:
\be
\zeta = \sqrt{{1\over 4}+\tilde{\Lambda}}~,
\ee
and the normalization constants $C_{\pm}$ are:
\be
C_{\pm} = {1\over 2}(\Delta\omega)^{{1\over 2}\pm\zeta}
e^{-{1\over 8}\pi M\omega} ~
{|\Gamma({1\over 2}\pm\zeta+{i\over 4}M\omega )|\over
\Gamma(1\pm 2\zeta)}~.
\ee
The wave functions eq.~\ref{eq:infwavefct} are generalizations of
the Coulomb functions to non-integer angular momentum. They are normalized
so that:
\be
\Phi^{\pm}_\infty \sim x^{-{1\over 2}\pm\zeta}C_{\pm}~,
\label{eq:phiplus}
\ee
for $\Delta\omega x\ll 1$ and:
\be
\Phi^{\pm}_\infty \sim {1\over x}\sin ({1\over 2}\Delta\omega x -
{1\over 4}M\omega\log x + {\rm const})~,
\label{eq:phiinf2}
\ee
for $\Delta\omega x\gg 1$.

\paragraph{The horizon region:}
In the horizon region we ignore the energy of the scalar field at infinity
and also the Coulomb type screening, due to the mass of the black hole.
Denoting by $\Phi_0$ the radial wave function in this regime
the radial equation becomes:
\be
{\partial\over\partial x}(x^2-{1\over 4}){\partial\over\partial x}\Phi_0
-{\tilde\Lambda}+{1\over x-{1\over 2}}~{1\over 4}
({\omega\over\kappa_{+}}-m{\Omega\over\kappa_{+}})^2
-{1\over x+{1\over 2}}~{1\over 4}({\omega\over\kappa_{-}}-
m {\Omega\over\kappa_{+}})^2]\Phi_0 = 0
\ee
The form of this equation is identical to the corresponding one for
the most general black holes in five dimensions~\cite{cl97a}.
This is in harmony with the intuition that the near horizon terms
express universal physics related to the underlying microscopic
structure. In particular the $SL(2,R)_L\times SL(2,R)_R$ symmetry of the
horizon region, exhibited for the five-dimensional case in~\cite{cl97a},
carries over to four dimensions.

The solution relevant in the following has only an infalling
component at the outer horizon. Taking the azimuthal quantum number
$m=0$ for typographical simplicity it is\footnote{We take $m=0$ in
the remainder of the paper. It can be restored by the replacements
$\beta_{R,L}\omega/2 \rightarrow \beta_{R,L}\omega/2 - m\beta_H\Omega$
and $\beta_H\omega\rightarrow \beta_H\omega-m\beta_H\Omega$.}:
\be
\Phi_0^{\rm in}=
({x-{1\over 2}\over x+{1\over 2}})^{-{i\beta_H\omega\over 4\pi}}
(x+{1\over 2})^{-{1\over 2}-\zeta}
F({1\over 2}+\zeta-i{\beta_R\omega\over 4\pi},
{1\over 2}+\zeta-i{\beta_L\omega\over 4\pi},
1-i{\beta_H\omega\over 2\pi},{x-{1\over 2}\over x+{1\over 2}})~.
\label{eq:phiin0}
\ee
We introduced the inverse Hawking temperature
$T^{-1}_H=\beta_H= {2\pi\over\kappa_{+}}$ and the corresponding
right (R) and left (L) components:
\bea
\beta_R &=& {2\pi\over\kappa_{+}}+{2\pi\over\kappa_{-}}
={2\pi\mu^2\over\sqrt{\mu^2-l^2}}
(\prod_i \cosh\delta_i+\prod_i\sinh\delta_i)~,
\\
\beta_L &=& {2\pi\over\kappa_{+}}-{2\pi\over\kappa_{-}} =
2\pi\mu (\prod_i \cosh\delta_i-\prod_i \sinh\delta_i)~.
\eea
A linearly independent solution can be chosen as the purely outgoing
wave, given by time reversal $\omega\rightarrow -\omega$.
The asymptotic behavior of $\Phi^{\rm in}_0$ at large $x$ can be
extracted, by using the modular properties of the hypergeometric
function $F$. It is:
\be
\Phi_0^{\rm in}\sim x^{-{1\over 2}-\zeta}
{\Gamma(1-i{\beta_H\omega\over 2\pi})\Gamma(-2\zeta)\over
\Gamma({1\over 2}-\zeta-i{\beta_L\omega\over 4\pi})
\Gamma({1\over 2}-\zeta-i{\beta_R\omega\over 4\pi})}
+x^{-{1\over 2}+\zeta}
{\Gamma(1-i{\beta_H\omega\over 2\pi})\Gamma(2\zeta)\over
\Gamma({1\over 2}+\zeta-i{\beta_L\omega\over 4\pi})
\Gamma({1\over 2}+\zeta-i{\beta_R\omega\over 4\pi})}~.
\label{eq:phiininf}
\ee

\paragraph{}

It is now straightforward to calculate the
absorption cross-section.
We take $A_\infty\Phi^{+}_\infty$ as the wave function in the asymptotic
region, and in some intermediate ``matching region'' we identify this with
$A_0\Phi_0^{\rm in}$, using eqs.~\ref{eq:phiplus} and~\ref{eq:phiininf}.
Postponing the justification of this procedure to the subsequent
section, the ratio of amplitudes becomes:
\be
|{A_0\over A_\infty}|= {1\over 2} (\Delta\omega)^{{1\over 2}+\zeta}~
e^{{\pi\over 8}M\omega}|\Gamma({1\over 2}+\zeta + {i\over 4}M\omega)|
~|{\Gamma({1\over 2}+\zeta-i{\beta_L\omega\over 4\pi})
\Gamma({1\over 2}+\zeta-i{\beta_R\omega\over 4\pi})
\over\Gamma(2\zeta)\Gamma(2\zeta+1)
\Gamma(1-i{\beta_H\omega\over 2\pi})}|~.
\ee
 From eq.~\ref{eq:phiinf2} we find the flux factor:
\be
{\rm flux}= {1\over 2i}(\bar{\Phi} r^2\partial_r\Phi-{\rm c.c.})
=  {\Delta^2\omega\over 16}|A_\infty|^2~,
\ee
at large distances; and from eq.~\ref{eq:phiin0} we find
the flux factor:
\be
{\rm flux}= {1\over 2i}(\bar{\Phi}r^2\sqrt{g^{rr}}\partial_r\Phi-{\rm c.c.})
={\beta_H\omega\Delta\over 8\pi}|A_0|^2 ~,
\ee
at the horizon. The effective two dimensional transmission coefficient
$|T_n|^2$ is the ratio of these two fluxes. Using a standard relation
from scattering theory we present the result as the absorption
cross-section of the $n$th partial wave:
\bea
\sigma^{(n)}_{\rm abs}(\omega) &=& {\pi (2n+1)\over\omega^2}|T_n|^2
\nonumber \\
&=& A~(2n+1)(\Delta\omega)^{2\zeta-1}
|{\Gamma({1\over 2}+\zeta-i{\beta_L\omega\over 4\pi})
\Gamma({1\over 2}+\zeta-i{\beta_R\omega\over 4\pi})
\over\Gamma(2\zeta)\Gamma(2\zeta+1)\Gamma(1-i{\beta_H\omega\over 2\pi})}|^2
\times \nonumber \\
&\times&
e^{{\pi\over 4}M\omega}|\Gamma({1\over 2}+\zeta + {i\over 4}M\omega)|^2~.
\label{eq:partabs}
\eea
In the intermediate step we used
${1\over 2}\beta_H\Delta = {1\over 2}S = A$ (which follows from
$G_N={1\over 8}$ and the last definition of $\Delta$
in eq.~\ref{eq:deltadef}.)

The absorption cross-section
is almost identical to the corresponding expression in five
dimensions~\cite{cl97a}; except for the presence of the last
term. In the limit where the effective angular momentum barrier
$\tilde{\Lambda}$ vanishes we have $\zeta\sim{1\over 2}$; so this
factor becomes:
\be
e^{{\pi\over 4}M\omega}|\Gamma(1+ {i\over 4}M\omega)|^2
={{1\over 2}\pi M\omega\over 1- e^{-{\pi\over 2} M\omega}}~.
\ee
The so-called Coulomb enhancement of the absorption is due to
long range attractive interactions of Coulomb type. It is well-known
from {\it e.g.} nuclear physics. Note that it is unique to four dimensions
where the gravitational potential falls off as $r^{-1}$.

\section{Estimates and Examples}
\label{sec:examples}
\subsection{Matching on constant potential}
We now determine the regime of validity of the absorption cross-section
eq.~\ref{eq:partabs}. The most generous condition arises when the
matching region can be chosen so that the effective angular momentum barrier
$\tilde{\Lambda}$ dominates over all other terms. This is matching on
a {\it constant} potential, in the parlance of~\cite{cl97a}.
The logic is that the asymptotic wave function can be used at large $x$,
the horizon wave function can be used at small $x$, and both are valid in
the matching region.

The precise condition is that there is a range of large $x$ so that:
\be
1\ll x~~;~
x^2 \Delta^2 \omega^2 \ll |\tilde{\Lambda}|~~;~
xM\Delta\omega^2 \ll |\tilde{\Lambda}|~~;~
{\beta_R \beta_L \omega^2\over x}\ll |\tilde{\Lambda}|
\ee
The necessary and sufficient conditions are that either:
\be
M\omega\gg |{\tilde\Lambda}|^{1\over 2}~~;~
\beta_R \beta_L M\omega^4\Delta\ll |{\tilde\Lambda}|^2  ~~;~
M\omega^2\Delta\ll |{\tilde\Lambda}| ~,
\label{eq:const2}
\ee
or:
\be
M\omega \tilde{<} ~|{\tilde\Lambda}|^{1\over 2} ~~;~
\beta_R \beta_L\omega^3 \Delta\ll
|{\tilde\Lambda}|^{3\over 2}~~;~
\Delta\omega \ll |{\tilde\Lambda}|^{1\over 2} ~.
\label{eq:const1}
\ee
In the S-wave ${\tilde\Lambda}\propto\omega^2$; so in this case
all the conditions are independent of frequency. This is reasonable
because in this case the only frequency dependence of the potential
is an overall factor that cannot influence the relative size of the terms.

In the calculation of the absorption cross-section we also assumed
that the $x^{-{1\over 2}+\zeta}$ term dominates over the
$x^{-{1\over 2}-\zeta}$ term in the matching region. The large value of
the matching $x$ is sufficiently to ensure this, provided $\zeta>0$.
In the regime where $\zeta$ is imaginary a closely related calculation
is valid. (It is given in the appendix of~\cite{mathur97}.)

\paragraph{Higher partial waves:}
The constant term in the potential is the effective angular momentum
barrier. Thus an important example is that of higher partial waves. In
particular, for any given background and perturbation frequency,
the partial wave number can be chosen so that ${\tilde\Lambda}\sim n^2$;
and moreover so that all the conditions eq.~\ref{eq:const1} are satisfied.
For natural frequencies $\omega\sim\beta_H^{-1}$ and generic black
holes ($\delta_i\sim 1$ and $l\sim\mu$) it is sufficient that $n\gg 1$.
This is interesting because the higher partial waves can be understood
microscopically from multi-particle
processes~\cite{strominger97a,mathur97b,gubser}. We will consider this
example further in the discussion in sec.~\ref{sec:discussion}.

\paragraph{Two large boosts:}
This case is the S-wave, with two large boosts
$\delta\sim\delta_i\gg 1$, and the other two boosts of order unity.
A background angular momentum of order $l\sim\mu$ may be included.
The inverse temperatures are comparable:
$\beta_R\sim\beta_L\sim\mu e^{2\delta}$; and
the other parameters are $M\sim\mu e^{2\delta}$,
$|{\tilde\Lambda}|\sim\mu^2 \omega^2 e^{4\delta}$, and $\Delta\sim\mu$.
The conditions eq.~\ref{eq:const1} are satisfied for all frequencies.

\paragraph{}
We note that the case of S-wave and one large boost violates the
conditions, even if the freedom to tune the angular momentum is employed.
In this case the absorption cross-section cannot be found in closed form.

\subsection{Matching on vanishing potential}

The calculation of Maldacena and Strominger~\cite{greybody} employed
matching on a {\it vanishing} potential. This is in general more
restrictive than the matching on a constant potential, but it also
provides a clearer distinction between the horizon terms, of presumed
microscopic importance, and the long range fields. In this case
there must be a range of large $x$ so that {\it all} the potential
terms can be neglected:
\be
1\ll x~~;~
x^2 \Delta^2 \omega^2 \ll 1 ~~;~
xM\Delta\omega^2 \ll 1 ~~;~
|\tilde{\Lambda}| \ll 1 ~~;~
{\beta_R \beta_L \omega^2\over x} \ll 1~.
\ee
The necessary and sufficient conditions are that either:
\be
M\omega\gg 1~~;~
|\tilde{\Lambda}| \ll 1 ~~;~
\beta_R \beta_L M\Delta\omega^4 \ll 1 ~~;~
 M\Delta\omega^2 \ll 1~,
\ee
or:
\be
M\omega \tilde{<} 1 ~~;~
|\tilde{\Lambda}| \ll 1 ~~;~
\beta_R \beta_L \Delta\omega^3 \ll 1 ~~;~
 \Delta\omega \ll 1~.
\label{eq:matchcond}
\ee
We have not found any significant example that takes advantage of the
first conditions, and a similar comment applies to scattering that is not
in the S-wave; so these possibilities will be disregarded.
Then the conditions eq.~\ref{eq:matchcond} are low energy conditions.

Matching on a vanishing potential automatically implies
$\zeta\sim{1\over 2}$; so the general absorption cross-section
eq.~\ref{eq:partabs} simplifies dramatically:
\bea
\sigma^{(0)}_{\rm abs}(\omega)
&=& A |{\Gamma(1-i{\beta_L\omega\over 4\pi})
\Gamma(1-i{\beta_R\omega\over 4\pi})
\over\Gamma(1-i{\beta_H\omega\over 2\pi})}|^2
~e^{{\pi\over 4}M\omega}|\Gamma(1+ {i\over 4}M\omega)|^2 \\
&=&
A~{\beta_L {\omega\over 2}\beta_R {\omega\over 2}\over\beta_H\omega}~
{e^{\beta_H \omega}-1\over
(e^{\beta_L {\omega\over 2}}-1)(e^{\beta_R {\omega\over 2}}-1)}
~{{1\over 2}\pi M\omega\over 1- e^{-{\pi\over 2}M\omega}}
\eea
The Coulomb enhancement factor will play no role in our discussion.
Next we consider some examples:

\paragraph{Low energy:}
All conditions are automatically satisfied when the wave length
$\lambda\sim\omega^{-1}$ is larger than all other scales in the problem.
In this case:
\be
\sigma_{\rm abs}(\omega\rightarrow 0) = A~.
\ee
This is the universal low energy absorption cross-section
(see~\cite{gibbons96} and references therein.)

\paragraph{Dilute gas regime:}
In this case three boosts are large $\delta\sim\delta_i\gg 1$ but the
last one is of order unity~\cite{klebanov96}. An angular momentum of order
$l\sim\mu$ may be included. The inverse temperatures are comparable
$\beta_R\sim\beta_L\sim \mu e^{3\delta}$; and the other parameters are
$M\sim\mu e^{2\delta}$,
$|{\tilde\Lambda}|\sim \mu^2 \omega^2 e^{4\delta}$, and $\Delta\sim\mu$.
The effective angular momentum barrier and the horizons terms
give the strongest condition on the frequency, namely
$\mu\omega e^{2\delta}\ll 1$. However this is still consistent
with the interesting regime
$\beta_R\omega\sim\beta_L\omega\sim 1$.

\paragraph{Near BPS black hole:}
Here all boosts are large $\delta\sim\delta_i\gg 1$. An angular
momentum of order $l\sim\mu$ may be included. There is a hierarchy
between the temperatures: $\beta_L\sim\mu e^{2\delta}$ and
$\beta_R\sim\mu e^{4\delta}$; and the other parameters are
$M\sim\mu e^{2\delta}$,
$|{\tilde\Lambda}|\sim\mu^2 \omega^2 e^{4\delta}$,
and $\Delta\sim\mu$. The horizon terms and the effective
angular momentum barrier both give the condition
$\mu\omega e^{2\delta}\ll 1$ on the frequency. This is consistent with
the structure in the range $\beta_R\omega\sim 1$ but not the other
interesting range $\beta_H\omega\sim\beta_L\omega\sim 1$.

\paragraph{Near extremal Kerr-Newman:}
The angular momentum is tuned so that $\mu^2-l^2=\mu^2\epsilon^2\ll\mu^2$,
but the charges are left general. In this limit
there is a hierarchy between the temperatures:
$\beta_L\sim\mu$ and $\beta_R\sim\mu\epsilon^{-1}$; and
$|{\tilde\Lambda}|\sim\mu^2\omega^2$, $M\sim\mu$, and
$\Delta\sim\mu\epsilon$. The strongest condition on the frequency,
from the horizon terms and the effective angular momentum barrier,
is $\mu\omega\ll 1$. This is analogous to the near BPS case: the
region $\beta_R\omega\sim 1$ can be probed, but
$\beta_H\omega\sim\beta_L\omega\sim 1$ cannot.

\paragraph{}

In five dimensions there are two angular momenta and it is possible to tune
them so that the inverse temperatures are large and
comparable~\cite{cl97a}. In this
limit the calculation is sensitive to all boost parameters. However in
four dimensions the angular momentum appears only in the R sector. It
plays no role in the estimates unless $l$ is tuned to be near $\mu$, and
this implies $\beta_R\gg\beta_L$; so there is necessarily a hierarchy
between the inverse temperatures. There is therefore no
``rapidly spinning black hole'' regime in four dimensions.

\section{Discussion}
\label{sec:discussion}
In the region where matching on a vanishing potential can be justified,
the Hawking emission rate is\footnote{We ignore the Coulomb-type
factor. Note that in regimes where it gives an enhancement of the absorption
cross-section it gives a {\it reduction} of
the emission rate. The naive application of detailed balance
that leads to eq.~\ref{eq:emrate} is modified by the presence of long
range interactions.}:
\bea
\Gamma_{\rm em}^{(0)}(\omega) &=&\sigma_{\rm abs}(\omega)~
{1\over e^{\beta_H\omega}-1}~{d^4 k\over (2\pi)^4}
\label{eq:emrate} \\
&=&
2\pi G_N~{\cal L}\omega~
{1\over (e^{\beta_L {\omega\over 2}}-1)(e^{\beta_R {\omega\over 2}}-1)}
~{d^4 k\over (2\pi)^4}~,
\label{eq:gammaem}
\eea
where:
\be
{\cal L}=
2\pi\mu^3 (\prod_{i=1}^4 \cosh^2\delta_i -\prod_{i=1}^4 \sinh^2\delta_i)~.
\label{eq:leff}
\ee
The emission rate eq.~\ref{eq:gammaem} is identical to the two-body
annhilation rate for quanta propagating on an effective string of length
${\cal L}$~\cite{mathur}. From our classical
calculation we expect that this microcopic model of the emission
process can be applied in the full range of validity (eq.~\ref{eq:matchcond})
of the two-body form of the emission rate (eq.~\ref{eq:gammaem}).
In particular, this includes the emission of very low energy quanta
from {\it all} black holes; so in this sense we can model all black holes
as effective strings, and their Hawking radiation as two-body processes.

However, it is only for special black holes that the two-body description
can be used at the energies of typical Hawking particles; and only for these
black holes is the emission spectrum eq.~\ref{eq:gammaem} applicable in
the range where it has characteristic features. In four dimensions there
is less flexibility than in five dimensions; so the characteristic
two-body features are only significant in regimes that involve
restrictions on the charges.

Eventually we would like to have a microscopic description of
all processes, at least in principle. However, at this point it seems
more rewarding to consider specific processes that go beyond the
S-wave of a minimally coupled scalar
field~\cite{cgkt,mathur97,strominger97a,mathur97b,gubser}.
Higher partial waves are particularly interesting because,
for sufficiently high partial wave number (eq.~\ref{eq:const1}),
their absorption cross-section can be calculated in the classical
theory for all black holes and arbitrary
frequencies\footnote{We ignore backreaction on the geometry and
ultimately this sets on both frequency and partial wave number.
Concerns have been raised that for this reason the microscopic
description of very high partial waves may not be
accurate~\cite{gubser}.}; and the result has a form that is characteristic
of string theory\footnote{These statements are
also true in the five dimensional case.}. The corresponding
emission rate can be written\footnote{As before we suppress the Coulomb-type
factor due to long range fields.}:
\bea
\Gamma_{\rm em}^{(n)}(\omega)
&=& ({8G_N {\cal L}\omega\over 2\pi})^{2n+1}
(2n+1){(2\pi)^2(n!)^2\over 8(2n)!^2(2n+1)!^2}
~
{\prod_{j=1}^n [({\omega\over 2})^2 + ({2\pi j\over\beta_L})^2 ]
\over (e^{\beta_L {\omega\over 2}}-1)} \times \nonumber \\
&\times &
{\prod_{j=1}^n [({\omega\over 2})^2 + ({2\pi j\over\beta_R})^2 ]
\over (e^{\beta_R {\omega\over 2}}-1)}
~{d^3 k\over (2\pi)^3}~.
\label{eq:nem}
\eea
This expression depends only on quantities that have a microscopic
interpretation: $\beta_{R,L}$ are the inverse temperatures of
the right and left moving string excitations, ${\cal L}$ is the
length of the effective string, and Newton's coupling constant $G_N$
is the $U$-duality invariant form of the string coupling. The angular
momentum of the black hole background enters only through $\beta_R$.
This is expected from a microscopic point of view, because here the
introduction of angular momentum is implemented as a projection acting
on the Hilbert space of the right movers. (In five dimensions there are
two angular momenta and they enter through $\beta_R$ and $\beta_L$,
respectively.)

In an effective string theory description the emission of a partial
wave with an angular momentum $n$ is dominated by an operator
that has dimension $n+1$, both in the right and left moving sectors.
It can be realized as a composite operator of $n+1$ free boson fields
(each boson can be traded for $2$ fermions). It is simplest to calculate
the thermal phase space factors of the initial string state in the
bosonic realization:
\be
I^{(n+1)}(\beta) = \int^\infty_{-\infty}
\delta ({\omega\over 2}-\sum_{i=0}^{n} p^i)~
\prod_{i=0}^{n}{p^i dp^i\over e^{\beta p^i}-1} =
 {1\over (2n+1)!}~{\omega\over 2}~
{\prod_{j=1}^n [({\omega\over 2})^2 + ({2\pi j\over\beta})^2 ]
\over (e^{\beta{\omega\over 2}}-1)}~.
\ee
(Useful relations are given in~\cite{gubser}.) The final state is the
$n$th partial wave of a minimally coupled scalar field. Microscopically
this corresponds a vertex operator of a scalar field with $n$
spacetime derivatives; so this gives a further
frequency dependence $\omega^n$ in the amplitude, and therefore
$\omega^{2n}$ in the rate. Finally, the normalization of the outgoing
state gives a factor $\omega^{-1}$. Collecting the factors, we arrive at
a microscopic interpretation of the frequency dependence of the emission
rate eq.~\ref{eq:nem}.

The dependence on coupling constant can be understood as follows:
in the bosonic representation there are $n+1$ operators on both the
right and left sides, and there is one outgoing state. The sphere
amplitude with these $2n+3$ vertices has a factor of
$g^{-2}g^{2n+3}=g^{2n+1}$; so the rate has a factor of
$g^{4n+2}\propto G_N^{2n+1}$. Moreover,
there is a supressed factor of ${\cal L}$ in the measure of
each of the phase
space integrals above, and the outgoing particle accounts for a factor
of ${\cal L}^{-1}$; so the dependence on the effective string length
becomes ${\cal L}^{2n+1}$. Dimensional analysis serves as a
check on these arguments. Combining these results we account for
eq.~\ref{eq:nem}, up to the numerical prefactor.

It would clearly be desirable to understand these arguments in the
framework of a detailed microscopic model. Specifically the numerical
prefactor of the emission rate should be calculable. However, already
in its present form the analysis indicates a striking connection
between the classical result and an effective string theory.

It is apparent from the preceding discussion that the emission rate
eq.~\ref{eq:nem} is closely related to similar ones that appear in
the context of near-extremal black holes. An effort to
understand these cases microscopically, including prefactor, is
far advanced and our discussion is adapted from this
context~\cite{strominger97a,mathur97b,gubser}\footnote{An important
issue in these calculations is the dependence on the volume of the
compact space. Our approach is manifestly duality invariant; so it
supports the resolution proposed in~\cite{mathur97b}.}. However,
our result generalizes these limiting cases: (i) it treats
all four charges independently, and no hierarchy between them is assumed,
(ii) it is {\it not} limited to near-extremal black holes,
(iii) it includes a background angular momentum, and
(iv) there is no low energy requirement. The expression eq.~\ref{eq:nem}
is nevertheless of the form that has been considered previously.
It is reasonable to assume that an effective string model can be devised
that accounts for the details of the limiting cases; and then our
classical result seems to indicate that the model will automatically
apply also in general.

\vspace{0.2in} {\bf Acknowledgments:}
This work is supported in part by DOE grant DOE-EY-76-02-3071, NSF
Career advancement award PHY95-12732 (MC), and NATO collaborative
grant CGR 949870 (MC).


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Great beer, great food, and great music; three simple ingredients that guarantee a good time. HarpoonFest delivered on all three accounts. Hundreds of people turned out to welcome in the summer season and sample some of the delicious beers that Harpoon Brewery has to offer. One of those beers is Harpoon's newest creation; Big Squeeze Shandy.
Whoever thought of combining grapefruit and beer deserves to win a Nobel Peace Prize. Now when it comes to beer, I'm not a huge citrus fan, but this beverage may just be one of my new favorite beers. The tartness of the grapefruit flavor, combined with the classic amount of barely and hops found in every Harpoon brew, create a whole new experience that my taste buds just couldn't comprehend.
This beer could reverse global climate change, make cats and dogs love each other, and create world peace. Okay, maybe I'm over reacting, but my point is that it's THAT good. I'm not the only one who thought so either. The Big Squeeze Shandy booth at HarpoonFest was by far the most popular.
So, with beer in hand, I decided to walk around and take in the atmosphere of this event. Everyone was friendly and happy and just having a good time enjoying the sounds of local bands like The Silks who were rocking out at the first stage I went to. I soon became hungry and stopped to grab a hot Italian sausage from The Sausage Guy; a Fenway Park staple who set up shop at HarpoonFest. This barbecued sausage paired perfectly with the Shandy I was drinking, furthering my belief that Big Squeeze Shandy is the perfect summer drink.
All in all I would call this beer festival a success. The pricing was average at $6 per beer ticket and the food was averagely priced as well; $6 for a sausage, $5 for a slice of pizza, no big deal. The experience was priceless though. Getting to taste great beers surrounded by friendly people who are enjoying themselves as much as you are was just awesome.
I will definitely be attending more of these in the future and recommend that every beer lover attend HarpoonFest. Sadly, the next one in Boston isn't until October when Harpoon Brewery hosts their annual Octoberfest, but if you can't wait that long, Harpoon Brewery is hosting their Championships of New England Barbecue festival in Windsor, Vermont July 26th and 27th.


text-to-speech communicators to be their lifesavers.
have literally saved their very lives when a parade balloon turned deadly.
wheelchair, so that Mary could communicate with her family.
Stephen Chamberlain. "But Sarah said, 'No. Mary needs to talk.'"
caused the tether lines of a giant, 500-pound balloon shaped like an "M&M"
received nine stitches in her head.
"If the Dynavox not been there, this could have been much worse," Mr.
either direction and this would have been a different story."
to repair or replace Mary's Dynavox communication device.


Read user comments about the side effects, benefits, and effectiveness of Zithromax intravenous.
This made my stomach hurt so bad. It worked for my symptoms but dang it hurt. I keeled over in pain the first time I used it. It helps to take with food.


text:
Will We Soon Have a Halberstam Street?
By Amy Derjue·	 4/8/2008, 10:17 a.m.
Get a compelling long read and must-have lifestyle tips in your inbox every Sunday morning — great with coffee!
Last month, Globe columnist Kevin Cullen wrote that Causeway Street should be renamed to honor sports legend Red Auerbach. The idea is still in its infancy, but Cambridge is working on its own plan to honor a legend of its own. A classmate of the late David Halberstam wants to rename Plympton Street to honor the journalist.
"I was contacted by a few of David's colleagues, who asked me, 'Do you think the city would like to do this?' " [former Cambridge City Councilor Frank] Duehay told [the Globe's Names column] yesterday. "I happen to like the idea, and I said I'd be happy to put it forth."
Halberstam's colleagues and friends chose Plympton Street since it's the home of the Harvard Crimson, the student newspaper where he served as managing editor during his time at Harvard.
Like every other journalist who has come of age in the post Baby Boomer era, we are fans of Halberstam. We'll keep you posted on how the notoriously wishy-washy Cambridge City Council handles the proposal.
The Power of Giving Back
All of the Amenities. None of the Alligators.
The Insider's Guide to Getting Out of a Parking Ticket in Boston
Market Basket Is Better Than Trader Joe's, a New Ranking Has Decreed
The Unlikely Rise, and Wide Appeal, of Boston's "Be a Man" Guy
Why Is Connecticut Always Excluded from Talk of New England?
A Love Letter to Market Basket's Instagram
Romance, Sex, and Street Parking
Is Boston America's Most Racist City? Ask a Black Bostonian for Once

redpajama_set_name: RedPajamaCommonCrawl


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My musings in this forum are an attempt to capture those moments before they slip away. Not all are my own, some are what I think someone else might be reflecting about and some are just my imagination!
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text:
CAMPUS DISCIPLINARY DEFENSE
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Starting from pole position after dominating all three practice sessions, Stoner beat Yamaha's world champion Lorenzo by 3.44 seconds at the Losail circuit in a dream debut with the works Repsol Honda team.
The Australian, who raced for Ducati last year, has now won 24 Grand Prixs in the top category.
Spain's Pedrosa, Stoner's Honda team-mate, was struggling with a painful arm and looked exhausted after finishing just over five seconds behind the Australian, despite taking the lead on the opening lap and fighting an entertaining duel to the halfway point.
Valentino Rossi of Italy, winner of nine world titles across the classes but struggling with a shoulder injury, finished well off the pace in seventh in his first race with Ducati after leaving Yamaha.
"Definitely, it couldn't be any better," Stoner told reporters. Lorenzo had warned that Stoner and Pedrosa were the men to beat, with Honda fastest at every pre-season test, and had said he would be happy to be on the podium.
The Mallorcan exceeded his own expectations and his delight was evident as he punched the air repeatedly as he cruised down the pitlane after taking the chequered flag.
On the victory podium, the Spaniard appeared the happiest of the three with the two Honda riders waving Japanese flags in solidarity with the victims of the devastating quake and tsunami.


text:
Manufacturers Betting on Hydrogen vs Electricity
November 13, 2019 November 13, 2019 BigRigVIN
Hyundai Motor Co. has an ambitious plan to wean the global trucking industry from fossil fuels by creating green commercial trucks with the same power and range as their diesel counterparts, choosing hydrogen over electricity.
The South Korean automaker unveiled the cornerstone of its strategy in Atlanta last month by showing the concept of its planned HDC-6 Neptune hydrogen fuel cell truck. Styled like a 1930s Art Deco steam locomotive, the truck could be plying U.S. highways by 2024.
Human-caused climate change dictates the end of diesel trucks, said Sae Hoon Kim, vice president of Hyundai's fuel cell center.
"This is about survival, and we don't have that much time to make this move," Kim said.
Hyundai plans to build a production capacity of 500,000 fuel cell systems for passenger and commercial vehicles by 2030 at a cost of about $6.4 billion.
While fossil fuel will be the primary energy choice for both passenger cars and commercial vehicles in the U.S. for years to come, other nations are already working to decarbonize transport.
Greater than 1/2 of Norway's new vehicle sales are electric cars according to the Wall Street Journal. Paris, Madrid, Barcelona, London and Rome all are preparing to ban either diesel or all internal combustion vehicles from their city centers over the next decade. Amsterdam wants to allow only emission-free vehicles by 2030.
Hyundai and a handful of rivals believe these diesel bans will provide the impetus for hydrogen commercial truck development.
Other truck and car companies also see hydrogen as a fuel of choice for transport.
Nikola Motor Co., a Phoenix startup, plans highway testing of its hydrogen fuel cell semi-tractor next year. Budweiser brewer Anheuser-Busch will test Nikola trucks in its fleet. The beer company said it plans to buy up to 800 of the hydrogen fuel cell models for its fleet of long-haul delivery vehicles.
Nikola also wants to remove risk from its customers. It will combine the major expenses of truck ownership and operation into a single monthly lease payment. But that deal requires a million-mile lease at the cost of 95 cents per mile, or $950,000 for the life of the contract – typically seven years.
Toyota Motor Corp., which makes the Mirai hydrogen fuel cell passenger car, also is developing commercial vehicles. It is providing fuel cell electric powertrains for a project with truck builder Kenworth. They are building 10 zero-emission Class 8 trucks. The project is part of a $41 million Zero and Near-Zero Emissions Freight Facilities grant from the California Air Resources Board. The vehicles will be used at the Port of Los Angeles/Port of Long Beach complex, primarily moving containers to and from California's Inland Empire region about 70 miles away. It is also testing a hydrogen fuel cell yard truck to move shipping containers within the Port of Los Angeles.
Even parcel giant UPS is dabbling in the field. It is developing a small fleet of hydrogen fuel cell delivery trucks. It wants 40 percent of the fuel it uses to come from sources other than conventional gasoline and diesel by 2025.
Companies are interested in hydrogen fuel cells because the technology could work well for freight and logistics, Antti Lindstrom, an analyst with IHS Markit said.
The fuel cell stack works like a mini power plant, converting hydrogen to electricity that can run the trucks. Drivers can fuel their vehicles almost as quickly as they can with diesel. The system is lighter than the power supply for a similar battery-electric truck.
"But without infrastructure, this is just an interesting technical experiment," Lindstrom said.
Trucking companies won't want to invest in hydrogen vehicles unless they know there will be places to get the fuel. Fueling companies don't want to invest in stations if there are no trucks on the road.
"It is a chicken or the egg example," Lindstrom said.
Hyundai believes it can solve the problem.
Its first commercial venture is in Switzerland. It has a joint venture to use 1,600 hydrogen fuel cell trucks to transport goods for Coop and Migros, Switzerland's two largest retailers. The vehicle will have a range of about 190 miles and will tow a 32,000-pound trailer. The trucks will get their power by pairing two of the 95-kilowatt fuel cell stacks Hyundai uses in its Nexo SUV. Deliveries start next year. All the trucks will be in operation by 2025, according to Maik Ziegler, Hyundai's fuel cell EV vice president.
An unusual road tax in Switzerland created a business case for producing the trucks and investing in a hydrogen fuel infrastructure, Ziegler said. Green vehicles are exempt from a Swiss tax on commercial vehicles that works out to about $1 per kilometer traveled.
It takes about 10 daily truck customers to create enough business to pay for a filling station, Ziegler said. That compares to about 200 passenger cars. When all the trucks are on the road, Switzerland will have a network of more than 150 hydrogen stations.
Hyundai plans to offer the trucks in a pay-per-use model. It's similar to an experiment Volvo Trucks is running with mine operators for autonomous trucking. Driverless Volvo trucks move rock from a mine to a port in Norway. The truck company gets paid by the load.
Such plans make sense for new technology, Ziegler said. They remove customer questions about the operating expense and resale value of new technology.
The strategy also is a way for the automaker to market its trucks against the battery-electric vehicles that will be its main rivals for green shipping. Hyundai is confident that hydrogen is a better way to store energy than batteries.
A truck in the heaviest Class 8 truck weight segment requires about 8 tons of batteries to have a 311-mile range, Kim said. A hydrogen system – including the fuel cell stack and tanks – weighs about 1.5 tons.
"It will have less weight so you can put more cargo on the truck," he said. That translates into higher profits.
Since refueling takes about the same amount of time as filling a diesel truck – much shorter than charging batteries – savings can be seen with faster delivery times.
Still, there are significant hurdles. One is infrastructure. But Ziegler said commercial contracts for hydrogen fuel cell trucks would pay to build that out. Nikola has the same belief. By default, the commercial market also creates a fueling network for hydrogen passenger cars.
The hydrogen also has to be produced using renewable systems, such as solar energy, or there is no environmental benefit, Kim said. Hyundai has a partnership with H2 Energy to build a supply chain for renewable hydrogen in Europe.
Hyundai believes fuel cell technology has applications beyond trucks and passenger cars.
"We are now developing buses, trams and small trains. We have some government development work for boats and shipping," Kim said. "A fuel cell is simply a power generator, and there can be many uses."
Blog, NewsBattery, Class 8, Diesel, Economy, Electric, Fuel, Fuel Cell, Heavy Duty, Hydrogen, Hyundai, Kenworth, Mack, Nikola, Range, Replacement, Toyota, Truck, Trucks
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Blue Pineapple Blog – Joy Matters. Gratitude Matters.
This latest act of violence has hit me hard.
I don't know if it's that it's the third one in this most recent string of events, or if it's because my own brother lives in Texas.
But as I sit here, with tears in my eyes, not even coming close to understanding the devastation, shock, loss, anger, sadness, loneliness and so many other feelings that the people in that church, the people in Sutherland Springs and their loved ones are feeling right now.
If I can't make sense of it, how can they?
With so much pain. With so many actions that we just cannot comprehend.
JOY MATTERS. More than ever.
"Why am I working so hard to decorate my son's birthday cupcakes like cute little Despicable Me minions when there are so many Syrian children starving to death? What difference do these stupid cupcakes really make?
Why am I enjoying the comradery of attending a football game at my alma mater while so many people have lost their lives? What difference does this stupid football game really make?
It matters because joy matters.
"Whether you're a full-time activist or a volunteer at your mosque or local soup kitchen, most of us are showing up to ensure that people's basic needs are met and their civil rights are upheld.
But we're also working to make sure that everyone gets to experience what brings meaning to life: love, belonging, and joy.
These are essential, irreducible needs for all of us.
And we can't give people what we don't have.
We can't fight for what's not in our hearts.
Instead of guilt, express gratitude.
In the midst of sadness, do something to bring someone joy.
That's what we are all called to bring to the world today.
ACKNOWLEDGE SOMETHING YOU ARE GRATEFUL FOR.
And let someone know. Share your gratitude.
FIND A WAY TO BRING JOY TO SOMEONE.
The smallest gestures can move mountains.
Share this message with a friend, a family member, a stranger.
Keep the joy and gratitude flowing.


BAGHDAD, Iraq, July 12 — Gen. George W. Casey Jr., the senior American commander in Iraq, said Wednesday that "terrorists and death squads" were responsible for the surge in sectarian killings here in recent weeks, and that there might be a need to move more American forces into the capital to prevent the deadly cycle from worsening.
His remarks came on a day when at least 30 people were killed and 37 wounded in and around Baghdad, including 20 people who were kidnapped from a bus station 60 miles north of the city and killed, Iraqi officials said. A local police official offered a slightly different account of that episode.
Hours before General Casey spoke, Iraq's prime minister, Nuri Kamal al-Maliki, told Iraqi lawmakers that his program of national reconciliation was the country's "last chance" to avoid slipping into chaos.
General Casey appeared at a news conference here with Defense Secretary Donald H. Rumsfeld, who made a surprise visit to American troops at an air base in Balad, north of Baghdad, before meeting with Mr. Maliki in the capital to discuss plans to improve this city's deteriorating security.
Mr. Rumsfeld said the number of Iraqi and American troops in Baghdad had increased to about 55,000 from 40,000 to deal with the surge in attacks in the city. But the increase has not noticeably restrained the sectarian bloodletting, mostly between Sunnis and Shiites.
The general said Sunni terrorist groups affiliated with Al Qaeda were killing Shiite civilians in Baghdad to show their continued power in the aftermath of an American missile strike last month that killed the leader of Al Qaeda in Mesopotamia, Abu Musab al-Zarqawi. In response to killings by Sunnis, he said, Shiite "death squads" in Baghdad had begun indiscriminately killing Sunni Arab residents, including dozens who were seemingly pulled from their cars and homes at random on Sunday and killed on the street.
"So you have both sides now attacking civilians, and that has caused the recent spike" in violence here in Baghdad, General Casey said. Foreign fighters, though, account for only a small percentage of the daily violence in Iraq; most of it occurs at the hands of nationalist and sectarian militias.
More than 130 people have been killed in or around Baghdad during the past four days, underscoring the persistence of violence that has convinced many Iraqis that the country is already in the throes of a low-level civil war.
On Tuesday, 50 people died in violence that included a double suicide bombing near busy entrances to the fortified Green Zone, scattered shootings, mortar attacks, a series of car bombs and the ambush of a bus with Shiite mourners returning from a burial.
The bodies of 20 people who had been reported abducted from a bus station in the tense city of Muqdadiya were found in a deserted part of a nearby village at 3:30 p.m. on Wednesday, Iraqi and American officials said. They had been blindfolded and shot, with their hands tied behind them, Agence France-Presse reported.
The victims' religious affiliations could not immediately be determined, nor could the motive for the killings, officials said. But a police officer in Muqdadiya, Amjad Hamid, said that the victims appeared to be Shiites and that the killings were apparently orchestrated by Sunni insurgents in retaliation for the abduction and killing of Sunni bus passengers at the same station hours earlier.
Dozens of armed men from the Mahdi Army, a potent Shiite militia, drove into the Muqdadiya bus station around 11 a.m. and rounded up 20 Sunni civilians, Officer Hamid said in a telephone interview Wednesday evening. Three bodies were discovered 500 yards away a short time later, he said.
Then, at about 12:30 p.m., he said, a group of Sunni insurgents stormed into a Shiite area of that city and seized 25 hostages, including, he said, a cousin of the provincial governor. He did not know whether they were the people who Iraqi and American officials said were kidnapped from the bus station and later killed.
In other violence on Wednesday, a suicide bomber walked into a popular restaurant in a mostly Shiite neighborhood in eastern Baghdad early in the morning and blew himself up, killing 7 people and wounding 31 others, the Interior Ministry said. Around 11 a.m., a car bomb exploded near a medical cotton factory in the northern part of the city, killing two civilians and wounding two others, the ministry said.
A battle also erupted between Iraqi policemen and gunmen in a predominantly Shiite neighborhood in southern Baghdad, killing one civilian and one policeman, said a Baghdad police official, who spoke on the condition of anonymity because he was not authorized to speak to the news media.
In a speech on Tuesday in Washington, the American ambassador to Iraq, Zalmay Khalilzad, said retributive sectarian violence had overshadowed the three-year-old Sunni insurgency as the single biggest challenge to the nation's stability.
Mona Mahmoud, Khalid al-Ansary and Khalid W. Hassan contributed reporting for this article.


text:
module SSHKit
  module Custom
    module Runner
      # A runner which executes all commands in sequence.
      class Sequential < Abstract
        # Executes all commands in sequence
        # @yields the actual host
        def apply_block_to_bcks(&block)
          backends.each do |backend|
            apply_to_bck backend, &block
            do_wait
          end
        end
      end
    end
  end
end

redpajama_set_name: RedPajamaGithub


text:
Haley Britzky Aug 31, 2018
Manafort associate Sam Patten charged in Mueller probe
Photo: Alex Wong/Getty Images
Sam Patten, a former associate of ex-Trump campaign chairman Paul Manafort, was charged on Friday for failing to register as a foreign agent for his involvement with a Ukrainian political party, Bloomberg reports.
Why it matters: This is yet another person taken down by the far-reaching Mueller investigation. And, as Axios' Mike Allen reported, there is still a lot of evidence the special counsel has — or could have — that we have yet to seen.
The details: Patten's felony charge, which he pleded guilty to, could lead to a maximum of five years in prison, per Bloomberg. The case was referred to the U.S. Attorney in D.C., Jessie Liu, spokesman William Miller told Bloomberg.
Patten admitted to helping donate foreign money to President Trump's Inaugural Committee, according to a separate Bloomberg report. Patten "enlisted a U.S. citizen to serve as a 'straw' buyer," in order to get a Ukranian client a ticket to the inauguration. The "straw" buyer bought four tickets for a total of $50,000, per Bloomberg. Patten won't be charged with this, as a part of his plea deal, Bloomberg reports.
Patten was paid "more than $1 million for Ukranian opposition bloc work," CNN reports, including meeting with Senate committee members and various lawmakers, as well as members of the executive branch.
During the 2014 election cycle, Patten worked with Cambridge Analytica. He also worked "for multiple political parties and office-holders in Ukraine."
He also reportedly worked for two U.S. senators, and was appointed as "senior adviser to the U.S. Undersecretary of State for Democracy and Global affairs" in 2008.
Patten had a "long friendship" with a Russian intelligence agent Konstantin Kilimnik, The Atlantic's Natasha Bertrand reported in April. Kilimnik also worked with Manafort and Rick Gates — both of whom have been prosecuted in the Mueller probe.
Read the charges:
Mueller investigation


text:
College Football Preview
Jacob Janousek, Staff Writer
photo courtesy of Sports Illustrated's Andy Staples
The college football season has arrived and sports fans are brimming with excitement. It has been too long since we have had some football to watch on TV and we have big games coming up like Alabama vs Florida State the first week. Now the big part of this season is the College Football Playoff and sport fans are putting their input on the season so here are my predictions.
The teams I feel will be left out is Penn State and USC (University of Southern California).Penn State has a lot of momentum coming into the 2017 season. They just won the Big Ten Championship and made a trip to the Rose Bowl. They will definitely be around number five by the end of the season, but with games against Ohio State, Michigan and Nebraska it will tough to come out the East and be Big Ten Champions and make the playoff
Now USC is also coming in with momentum after winning the Rose Bowl against Penn State last season. They are looking to come out as Pac 12 Champions with All- American quarterback Sam Darnold, but that may not make them in the playoff. The USC schedule just looks too tough to win out and they don't have enough tough game which ultimately doesn't help their resume to get into the playoff. Stanford is a hump to get over because they are successful. I just feel the Pac 12 isn't very strong and that will leave them out of the playoff.
Who makes the cut?
This may be a surprise, but Oklahoma State has a very good chance to to jump in. They start out at ten in the AP poll and have a season where they all favorite, they will play for ranking teams this season (#23 Texas, #22 West Virginia, #7 Oklahoma and #20 Kansas State). Their hump would be Oklahoma, but they get them at home and if they get over that they may have the play Oklahoma again in the Big 12 Championship but with a receiver core including All American James Washington they are fast and productive that will get them to the playoff at that number four spot.
Florida State has momentum coming into the season being ranked third in the preseason AP Top 25. They won against Michigan last year in the Orange Bowl. They start off this year against Alabama most likely to lose but they still will make the playoff. Deondre Francois is coming in looking like he could be ACC player of the year.
Ohio State ended the season with no momentum at all last season. They made it to the college football playoff and didn't play well. They lost 31-0 to the eventual National Champion Clemson. This year is a new team with a goal to get better. J.T Barrett looks to be a Heisman candidate and lead the Buckeyes back to the Playoff. This year their humps are Penn State and Michigan. Penn State beat them last year and they ended up winning the Big Ten. I feel Ohio State may lose one of this games, but still make the #2 spot in the Playoff.
Now this one should be obvious. Alabama is one of the best college football programs in the country. They have gone to every college football playoff and why not be able to do it again. They are preseason #1 and look to steam roll the SEC and make it to the number one spot in the College Football Playoff.
Lamar Jackson QB, Louisville
Lamar Jackson is the reigning Heisman Trophy winner from last season and looks to do it again. He will be stronger and more athletic after a whole off-season of work and studying film. He may be the best in the NCAA because all of his competition was drafted in the NFL. There is always a surprise person every season to make a run at the Heisman but Jackson will he too good.
Jacob Janousek, Sports Director
Jacob is a senior and is in his second year on the CATalyst and MWHS Wildcats News staff. He is very involved in the STRIV program and will be commentating...
Millard United Rugby takes the State Title
Millard West track races through the NSAA State track meet
Cats Capture First State Championship
Last Stop on the Road to State
West Wins it All
Time for State: A look back on the baseball season
Districts: Win or go Home
The Wildcats pounce on the Monarchs
Don Kraft Varsity Baseball Invitational


text:
Howie Carr is the New York Times best-selling author of The Brothers Bulger and Hitman, in addition to several other Boston organized-crime books and two novels. He is the host of a New England-wide radio talk-show syndicated to more than 20 stations, and is a member of the Radio Hall of Fame in Chicago. He is also a columnist for the Boston Herald, and has won a National Magazine Award for Boston Magazine. He is also a contributor to Breitbart.com.
Boston organized-crime boss Whitey Bulger was so infuriated by Carr's groundbreaking reporting that he once put out a murder contract on Carr, a story detailed on 60 Minutes. At his 2013 trial on murder and racketeering charges, Bulger tried to have Carr banned from the courtroom by calling him as a defense witness. Now imprisoned for life in Arizona, the crime czar still says his greatest regret was not murdering Carr when he had the chance. Carr once taught a course at Harvard, where he had to cross a picket line against himself to get to his class.
Tweets by HowieCarrShow


Building your own arcade is fun, building it and sharing your thoughts is even more fun! If you have questions that even the wiki cannot answer, take a look at the community. The articles in this section can give you some pointers and insight in the BYOAC community.
A lot of people will look at an arcade cabinet and say "Hey, that looks easy- it's just a screen, some wood and some buttons.", but arcade cabinets aren't quite as simple as many people think. Here's a good place to start learning about the various ins and outs of arcade machines in general.
Looking for ideas? Looking for ideas to avoid? Check out the pages of all those brave enough to take the plunge and build.
Good construction work requires planning. This is also true for building a cabinet. With decent construction plans and button layout plans things are much easier. This section gives you a nice overview of software tools that can help you in constructing your own cabinet.
If you're planing on building an arcade cabinet from scratch, these are some of the materials you might end up using for various elements of the cabinet.
Building your own arcade machine is no simple task and requires the correct tools as well as the knowledge of how to use each one correctly and safely. Hopefully you already own some of these tools and are well versed in their operation. If not, here's a few things you might want to add to your shopping list.
Vendors: Who do you buy your stuff from?
Various options are available to display the games you wish to play. Browse these sections to learn more about those options.
So, you've build your cabinet and hooked everything up. Now it is time to get everything configured so you can actually use your cabinet!
Once you have built a real cabinet you probably want to hide the fact that there is a regular PC powering it. In that case you will need a graphics fullscreen frontend. This way you can keep the arcade look and feel and still select your favorite game or emulator. While you are at it, you might even consider running other applications such as jukebox software!
Nostalgia comes in many different flavours. Do you wish to replay an old arcade game or recapture that classic console game feel? Take a look at this section to find out how to get your cabinet to play the games you like!


Just before Christmas I have been shopping at H&M… and my shopping spree was so succesful! I have bought three sweaters and two dresses! Today I show you the second dress I bought back then… the leopard print dress!
This entry was posted in Fashion, Winter and tagged dress, Fashion, H&M, leopard print, outfit, Winter.
This week in the outfit of the week a lovely print… polkadots! When I saw this dress in H&M recently I immediately was drawn to it for two reasons: the lovely green colour and the polkadots! Read more about this polkadots dress!
This entry was posted in Autumn, Fashion, Outfits and tagged dress, Fashion.
The fifties definitely brought some stylish trends… like the pencil dress. And today's outfitpost will take you back to those happy days in a flash! Read more about this fifties-inspired dress!
This entry was posted in Autumn, Fashion, Outfits and tagged dress, Fashion, mad men, outfit.
This black 'n white summer dress… I must admit that I really have been wanting to chuck it out several times, but everytime it ends up on the 'maybe' pile and thus back in my wardrobe.. and every summer I wear it several times and I'm glad that I haven't thrown it out just yet… Read more about this black 'n white summer dress!
This entry was posted in Fashion, Outfits, Summer and tagged dress, Fashion, mcgregor, outfit, outfit of the week.
Last Saturday I wore my mini black 'n white dress with a black turtleneck underneath. In today's post, I style three black 'n white dresses… with an orange coat, a red long cardigan and a teal fake fur. Which style do you prefer? You can vote in the poll below the images!
This entry was posted in Autumn, Fashion, How to and tagged dress, Fashion, how to wear.


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And once you're out of training, the support doesn't stop. We continue to provide you with marketing and training support, including internet marketing, montly training conference calls, a frequently updated operations manual, and a yearly conference where the whole franchise comes together.


Back by popular demand, the hugely successful abc Signalling in the Age of Steam details the theory and practice of signalling.
Following the massive success of the first edition, Colin J Marsden presents this fully up-to-date guide for all modern traction enthusiasts.
Available in hard back for the first time, BR Rail Atlas 1947 reminds readers of a time when railways were still one of the most popular forms of transport.
Informative, up-to-date, practical and entertaining, the latest edition of 'Football Grounds from the Air: Then & Now' is a must have buy for any serious football fan.
Responding to a growing international market in Nazi medal dealing and collecting, this new book gives practical advice on recognition, authenticity, values and best practice, together with an excellent selection of photographs.
Covering the developments in signalling practice in the UK, this pocket guide contains information on the signalling in use on the CTRL and, includes colour photographs.
A large format book that portrays the aircraft and camouflage and markings of the various aviation arms of the Italian Regia Aeronautica. It covered: day fighters, bombers, dive-bombers and ground-attack units and aircraft and maritime and transport aircraft. It also covers the history of the Italian Regia Aeronautica.
A highly illustrated history of one of the most controversial British aircraft designs of all time whose cancellation still generates comment over 40 years after its abandonment.


The site of a horrific mass killing will become a house of worship again.
Emanuel African Methodist Episcopal Church in Charleston, South Carolina, will hold a service at 9:30 a.m. Sunday, according to CNN affiliate WCSC.
Authorities said Dylann Roof, 21, of Lexington, South Carolina, admits he shot and killed the people he'd sat with for Bible study at the historically black church, two law enforcement officials said.
Roof is white and all the victims are black. He told investigators he did it to start a race war, according to one of the officials.
The church premises remained a crime scene, and thus off-limits to church members, until Charleston police released it Saturday.
At 10 a.m. Sunday, many churches plan to ring their bells, WCSC reported.
"When something this horrendous happens this close to home, you are compelled to do something," event coordinator Dorsey Fairbairn said on the Facebook page.
That message was echoed by Arthur Hurd, the husband of victim Cynthia Hurd. He's in the Merchant Marines and arrived in Charleston on Saturday.
Once they passed the church, the group filled Charleston's iconic King Street, usually packed with tourists this time of year. Many carried signs of support for the victims of the Charleston shooting and the black community: "STILL WE RISE," "Hand in Hand," "Do the right thing," "Black Lives Matter," signs read.
The website, called the Last Rhodesian, is bare bones. Roof's name doesn't appear anywhere on the site but he is shown in many of the photos. An Internet ownership search shows the website was registered to Roof and listed as the administrator.
While the nation rallies behind Charleston, an insight into Roof's state of mind came from Charleston County Sheriff's Office spokesman Maj. Eric Watson.
Funeral plans for Pinckney, who was a state senator, were announced Saturday.
Pinckney's casket will be at the State House rotunda lobby from 1-5 p.m. Wednesday. Public viewings will also be held Thursday at St. John AMC Church in Ridgeland and Emanuel AME Church.
The funeral will be held at 11 a.m. Friday at TD Arena on the College of Charleston campus. The service is open to the public.
CNN's Andy Rose, Ed Payne, Brian Todd, Betsy Klein, John Couwels, Carma Hassan, Dugald McConnell, Natisha Lance and Paul Murphy contributed to this report. CNN's Ralph Ellis and Greg Botelho wrote in Atlanta.


Who do you listen to when you go to Trader Joe's and don't want to carry your groceries up the stairs? Junglepussy. Who do you listen to when you want to grow? Junglepussy. Who do you listen to when you realize your ex-boyfriend never took you to the zoo? Junglepussy.
She can rap, she can act, and she can model. Sure, there are others who can do that too but they aren't Junglepussy. She is in a league of her own.
People knew Junglepussy was special with Satisfaction Guaranteed (2014) and Pregnant with Success (2015). She headlined WVAU's 2016 spring semester show. We saw the vision.
Early songs like "Cream Team" and "Bling Bling" set the tone for the type of person she is. Confident, opinionated, and a damn good rapper. Her latest album, Jp3, sealed the deal. It dropped in May and she has been on a whole new level ever since. Jp3 will likely make it onto end-of-year lists, so get ahead of the game by listening to "Trader Joe", "I'm in Love", and "Showers".
As a New York native with Caribbean roots, Junglepussy loves her city and spreads the love too. Her social media accounts are a hub for witty jokes and motivation. Her all-caps tweets remind you of your worth; "THE SILLIEST THING U CAN DO IS ACT LIKE YOU KNOW ME". You may not know Junglepussy personally, but after listening to her music you definitely want to.
Catch her on the NYFW runway, cracking jokes on the big screen, and performing on The Junglepussy USA tour. She stops by DC on October 18th at Songbyrd Music House for a concert presented by Songbyrd and Capitol Sound. Tix on sale now.
If you don't come to her concert at Songbyrd, well… Junglepussy has a tweet for that too: "WHY WOULD I CARE TO BE LIKED BY TERRIBLE PPL WITH BAD TASTE?" Don't be a terrible person with bad taste, get a ticket.


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Digital BANDA has consultants who guide companies through the analysis and implementation phases, and can take responsibility for both running the process and supporting the client's own staff. We have helped such clients as the Tax Administration, Welfare Service etc.
When you what you want to accomplish our experts or consultants have the tools and methods that allow you to reach all the way to success. We help you to define and illustrate your goals. This facilitates the identification of processes, policies, concepts and resources which are necessary to achieve your predefined goals.
Change Management: A new IT system in itself rarely confers any benefit before being implemented in the organization. Therefore, change management is the key to realizing the potential of your company's IT investments. Digital Banda helps companies with efficient and proper use of new or altered systems by adapting work processes and motivating employees for change.
Digital Marketing Training Institute: Digital Banda is also serving as one of the Best Digital Marketing Training institute in Lucknow. We provide real time and result oriented Digital Marketing course in Lucknow. Training course of our digital marketing course is designed from basic to advanced level. We have dexterous team of experienced professionals who will aware you with the real Digital Marketing world, which provides Digital Banda an edge over other Digital Marketing training institutes. Digital Banda has designed its course content for students as well as professionals to get the placement in major MNC companies as soon as they complete the Digital Marketing training course. Digital Marketing training in Lucknow conducted by Digital Banda is delivered on short term as well as long term basis. We provide you Digital Marketing training on live projects.
Digital Banda provides Digital Marketing Training in Lucknow not only in vacations but all days of year. You can achieve this training along with your regular studies.
The Best part of our institutions which makes us different from others institutions is we provide you Google certifications along with Digital Marketing Diploma certificate.