text:
Q: Inject service without using constructor I am trying to create a generic http service that would do all basic http requests. So, the service might look like this:
export class GenericService {
constructor(
private http: HttpClient
) {
  this.data();
}
data() {
  return this.http.get(`${environment.apiUrl}/..../`)
    .pipe(map(data => {
    return  data;
  }));
 }

}
I then want to create a data pipe that I will extend every component with. That class might look like this:
  export class DataPipe implements OnDestroy {
  subscription;
  constructor(private dataSvc: GenericService) {
  }
  getData(source: any) {
  this.subscription = this.dataSvc.data()
    .subscribe(data => {
    source = data;
  });
  }
  ngOnDestroy() {
    this.subscription.unsubscribe();
  }
 }

Finally, a component:
    export class Component extends DataPipe {
    source: any;
    constructor() {
     super(GenericService);
   }

   getData(source);
 }

I am assuming that the "source" that is passed to getData() will get actual value. Even if it worked, I am getting an error at super(GenericService); since GenericService's constructor expects a parameter. Ideally, I wouldn't even want to deal with GenericService in a component. All a developer needs to know is to extend his component with DataPipe class and call getData(). Am I even going to the right direction with such architecture?
Thanks

A: I want to inform you.

*

*HttpClient is a singleton service in the whole project, if you imported HttpClientModule in the app.module.ts,

*requests made by HttpClient, they will be closed automatically after receiving a result from the server.
I recommend you simply import the service and call the function (which will send request to the server) from component where you need to get the necessary data from server
Here is the simple example.
https://stackblitz.com/edit/call-http-request-in-angular-6-cwrdrr?file=src/app/app.component.ts


text:
End of the line for Le Clos Jordanne Pinot Noirs and Chardonnays: The brand is dead
An exciting chapter in Canadian winemaking at the highest level has, sadly, come to end with new the venerable Le Clos Jordanne brand ceasing to exist as of the current 2012 vintage.
Del Rollo, senior director of government relations and estates for Constellation Brands, owner of Le Clos Jordanne, confirmed the shocking news to Wines In Niagara on Tuesday.
"It wasn't an easy decision," said Rollo, "but it makes sense and we have a robust plan for the future."
Rollo said that an announcement is coming soon as to what will become of the former Le Clos Jordanne and the fruit grown at its three key vineyards – Le Clos Jordanne Vineyard, Claystone Terrace and Talon Ridge. He said a new wine will emerge from the coveted vineyards. "I'm pretty excited to know there will be something new," he said.
Rollo said two short crops in a row (2014-2015) prompted the decision to do away with the brand, along with some other key factors that, at the end of the day, didn't make the top-quality and critically acclaimed Pinots and Chards from Le Clos a smart business decision.
"I have a personal connection to Le Clos, so it does make me sad," he said. "But I have mixed emotions." He said he's excited by what's coming. He added that there is no current plan "that I know of" to sell the vineyards.
Original winemaker at Le Clos, Thomas Bachelder, called the project "the promise of Niagara" and said the vineyards, without question, are "some of the best in Canada" for Pinot Noir and Chardonnay.
Bachelder went on to his Bachelder wine project after Le Clos and Sebastien Jacquey, above, took over for him. Jacquey has since joined Megalomaniac as the winemaker there and the Le Clos brand moved to the main Constellation Brand winery in Niagara Falls.
Bachelder said buying vineyards isn't in his business plan, but they were, Le Clos would be on top of his wish list.
"Someone's going to get those vineyards, some day," he said. "It's amazing (that the brand has closed), but the Phoenix will rise from the ashes."
More to come on this breaking story.
About Le Clos:
Le Clos Jordanne was inspired by an original initiative by Inniskillin cofounders Donald Ziraldo and Karl Kaiser. In 1993, Inniskillin entered into a joint venture with Burgundian producer Jaffelin. Together they created limited edition VQA wines called "Alliance" made from Pinot Noir and Chardonnay grapes grown in Niagara. This reinforced Canada's ability to grow cool climate varieties in the Niagara region that are well known and respected in Burgundy, France. The collaboration combined the expertise of winemakers Bernard Repolt from Jaffelin and Karl Kaiser from Inniskillin. The distinction of these wines were based on barrel selection and vineyards that were producing the best fruit for these varietals. The wines were made until 1997 with Chardonnay being produced every year and the Pinot Noir only being made in the very best vintages (93, 95, 97).
The success of Inniskillin's joint venture led Donald Triggs, wine pioneer and CEO of Vincor, the company that owned Inniskillin and Jackson-Triggs Wines, to continue developing their relationship with Jaffelin, who had since then become a part of Boisset Wines. Together, they conducted careful research across the Niagara region, hand selecting vineyards that would be properly suited for growing ultra premium cool climate grapes. Specialty Chardonnay and Pinot Noir rootstock was imported from France and expertly planted in the chosen vineyards. The combined winemaking expertise and passion of Boisset's Pascal Marchand and Vincor's Thomas Bachelder, ensured that no detail was overlooked in paying respect to the time honoured traditional vineyard and winemaking techniques used in Burgundy, France.
EXCLUSIVELY PINOT NOIR AND CHARDONNAY
Le Clos Jordanne's objectives were to show the similarities between Niagara and Burgundy and yet at the same time reveal the uniqueness of the Niagara Terroir. Throughout the range of wines, Le Clos Jordanne wanted to minimize the winemaking intervention and focus on the vineyard differences. The Niagara region is ideal for growing early ripening grape varieties, such as Pinot Noir and Chardonnay, which are the key noble grape varieties in Burgundy, France. Furthermore, Pinot Noir and Chardonnay, with their thin skins, have the sensitivity required to express their own growing conditions with precision and elegance.
Niagara's Ravine Vineyard: Where the magic happens
Last call for a ground-breaking Niagara wine brand: RIP Le Clos Jordanne
Chuck Byers
Sad day for Ontario (Canadian) wine. Le Clos was an inspiration to not only Ontario and Canadian wine but wine vineyards world wide. So sorry to hear of its passing!
It was a treasure!
Robert Gravelle
Yes, very sad indeed. I'm a Toronto based Sommelier/wine buyer and have always wanted to be an advocate for Ontario wines but truthfully have felt that buying local was always a challenge. I generally felt that I could get behind about 5% of Ontario juice, with wineries like Stratus, Tawse, Hidden Bench and of course, Le Clos Jordanne being the constants. Seeing Le Clos Jordanne being sold in the Ontario only shops was a bit exciting at first but soon it was evident that they didn't belong there. The quality of their wines (with markedly higher price tags, too) was out of line with the other very middling stuff you'd find there. It was often marked down as well, again good for me but a bad sign. I felt like the appearance of this high quality wine amongst the rest of the plonk was perhaps the kiss of death for LCJ. It's a shame, it will be missed.
The short crop excuse is BS… This was in the works for years.
That's what happens when US based businesses buy out Canadian owned manufacturing. They focus on making money, whereas Canada has always focused on quality. So sad………

redpajama_set_name: RedPajamaCommonCrawl


Zeiger, Roni F.. "Hyperthyroidism." Diagnosaurus, 4th ed., McGraw-Hill Education, 2014. Emergency Central, emergency.unboundmedicine.com/emergency/view/Diagnosaurus/114311/all/Hyperthyroidism.
Zeiger RF. Hyperthyroidism. Diagnosaurus. 4th ed. McGraw-Hill Education; 2014. https://emergency.unboundmedicine.com/emergency/view/Diagnosaurus/114311/all/Hyperthyroidism. Accessed April 20, 2019.
Zeiger RF. Hyperthyroidism [Internet]. In: Diagnosaurus. McGraw-Hill Education; 2014. [cited 2019 April 20]. Available from: https://emergency.unboundmedicine.com/emergency/view/Diagnosaurus/114311/all/Hyperthyroidism.


AS of today they shutdown that practive... at least for free.
Browsing thru this forum you will notice some images missing in some topics and some of them, if not all, are stored at Photobucket.
If any of you have any other alternative to image hosting for free just leave your sugestion in this topic.


text:
\section{Introduction}

Closed time-like curves (CTCs) in solutions of General Relativity can pose challenges to Hawking's chronology protection conjecture. It is well known that Kerr metric has CTCs; however, they are hidden inside the event horizon, and hence obey the chronological censorship. The G\"odel metric \cite{Godel:1949ga}, a solution of cosmological Einstein gravity coupled to some uniform pressureless matter, describes a homogeneous rotating universe that has naked CTCs and has no globally spatial-like Cauchy surface.  However, the fine-tuning balance between the cosmological constant and the matter density in G\"odel universe makes it an unrealistic model to challenge the chronology protection.  Nevertheless it is a good toy model to study the effects of naked CTCs in both classical and quantum gravities.

The study of CTCs has enjoyed considerable attention with the development of the string
theory and the AdS/CFT correspondence.  Large number of supersymmetric or non-supersymmetric
G\"odel-like solutions, including also black holes and time machines, with naked CTCs were constructed in gauged supergravities in higher dimensions,
see e.g.~\cite{Barrow:1998wa,Gauntlett:2002nw,Herdeiro:2002ft, Boyda:2002ba,%
Harmark:2003ud,Takayanagi:2003ps,Brecher:2003rv,Brace:2003st,Gimon:2003ms,Israel:2003cx,
Cvetic:2005zi,Banados:2005da,Wu:2007gg,Barnich:2005kq,Peng:2009ty,Wu:2011im}.  These works raise important issues whether the problems of CTCs may be resolved by stringy or quantum considerations, or whether naked CTCs in the bulk implies the breakdown of unitarity of the field theory.

In this paper, we focus on the original four-dimensional G\"odel universe that is a direct product of a line and a three-dimensional metric \cite{Godel:1949ga}
\begin{equation}
ds^2 = \ell^2 \Big(-(dt + r d\phi)^2 + \ft12 r^2 d\phi^2 + \fft{dr^2}{r^2} + dz^2\Big)\,.\label{godelmetric}
\end{equation}
This metric is an exact solution of the Einstein equation involving some uniform pressureless matter
\begin{equation}
R_{\mu\nu}-\ft12 R g_{\mu\nu}+ \Lambda g_{\mu\nu} = T^{\rm mat}_{\mu\nu}\,,\qquad
\Lambda=-\fft1{2\ell^2}\,,\qquad T^{\rm mat}_{\mu\nu}=u_\mu u_\nu\,,\label{pfluid}
\end{equation}
where $u^\mu =(\ell^{-2},0,0,0)$. G\"odel universe has enjoyed continuous interests in
the general-relativity community, (see, e.g.~\cite{Banerjee,Bampi,Raychaudhuri:1980fd,%
Reboucas:1982hn,Reboucas:1986tz, Reboucas:2009yw,Agudelo:2016pic},) and G\"odel metric (\ref{godelmetric}) were generalized to G\"odel-type metrics where coefficient $\ft12$ in (\ref{godelmetric}) is replaced by a generic constant $\alpha$.  To avoid pedantry, we shall refer {\cal all} these metrics as G\"odel metrics, which are distinct from those afore-mentioned G\"odel-like metrics. It turns out that most theories associated with these general G\"odel metrics involve energy-momentum tensor of some uniform pressureless matter. Electric and magnetic fields periodic in $z$ as a replacement for such matter were used to construct G\"odel metric in \cite{Reboucas:1982hn}, where $z$ is a circular coordinate.  It is worth mentioning that the three-dimensional metric with $dz^2$ removed can arise as an exact solution of Einstein-Maxwell theory with a topological term $A\wedge F$ \cite{Banados:2005da}.  The embedding of the three-dimensional metric in heterotic string theory was first given in \cite{Israel:2003cx}.

The main purpose of this paper is to construct more Lagrangians that admit G\"odel metrics as exact solutions. We present three Lagrangians that admit the G\"odel metrics as solutions, all involving only the fundamental matter fields.  These are Einstein-Maxwell-Axion (EMA), Einstein-Proca-Axion (EPA) and Freedman-Schwarz \cite{Freedman:1978ra} $SU(2)\times SU(2)$ gauged supergravity theories. The Freedman-Schwarz model can be obtained from the effective actions of string theories via the Kaluza-Klein reduction on $S^3\times S^3$.  Thus the four-dimensional G\"odel universe can be embedded in string theory.

The paper is organized as follows. In section 2, we give a review of G\"odel metrics and their properties.  We also show that for appropriate choice of parameter, such a metric can also describe a direct product of time and a squashed 3-sphere.  In section 3, we construct EMA and EPA theories that admit G\"odel metrics, and also solutions involving squashed 3-sphere.  We generalize the theories to higher dimensions and also give the effective three-dimensional theories by Kaluza-Klein reduction.  In section 4, we consider double Wick rotations and obtain two types of black hole solutions.  In section 5, we show that G\"odel metrics are exact solutions of the Freedman-Schwarz model and hence obtain the corresponding ten-dimensional solutions of string theories.  We conclude the paper in section 6.

\section{G\"odel universe}

\subsection{The metrics of G$_\alpha \times \mathbb R$}

In this paper, we consider a class of metrics in the following form
\begin{equation}
ds^2 = \ell^2 \Big(-(dt + r d\phi)^2 + \alpha r^2 d\phi^2 + \fft{dr^2}{r^2} + dz^2\Big)\,,\label{gvac}
\end{equation}
where $\ell$ and $\alpha$ are constants.
The metric is a direct product of $\mathbb{R}$ associated with the coordinate $z$ and the three-dimensional metric of $(t,\phi,r)$, which we shall call G$_\alpha$. The original G\"odel metric \cite{Godel:1949ga} is recovered when we take $\alpha=\ft12$, corresponding to G$_{1/2}\times \mathbb{R}$.  To avoid pedantry, we shall refer the metric (\ref{gvac}) with generic $\alpha$ also as the G\"odel metric.

In addition to the constant shifting symmetry along the $(t,\phi,z)$ directions,
the G\"odel metric (\ref{gvac}) is invariant under the constant scaling
\begin{equation}
r\rightarrow \lambda r\,,\qquad \phi\rightarrow \lambda^{-1} \phi\,.\label{scaling}
\end{equation}
Note that imposing this scaling symmetry also implies that $\phi$ describes a real line, rather than a circle.  This scaling property indicates that the metric is homogeneous.
Since the metric G$_\alpha$ is three dimensional, its curvature is completely determined by the Ricci tensor, whose non-vanishing components are given by
\begin{equation}
R^{\bar 0\bar 0} =\fft{1}{2\alpha \ell^2}\,,\qquad R^{\bar 1\bar 1}=\fft{1-2\alpha}{2\alpha \ell^2}=R^{\bar 2\bar 2}\,.
\label{ricci-curv}
\end{equation}
Here we present the curvature in tangent space with the vielbein
\begin{equation}
e^{\bar 0} = \ell (dt + r d\phi)\,,\qquad e^{\bar 1}=\ell \sqrt{\alpha}\,r d\phi\,,\qquad
e^{\bar 2}= \fft{\ell dr}r\,,\qquad e^{\bar 3}=\ell dz\,.\label{viel}
\end{equation}
It is clear that when $\alpha=1$, the metric is locally AdS$_3$ (3-dimensional anti-de Sitter spacetime), i.e. G$_1=$ AdS$_3$.

\subsection{Energy condition and $\alpha$ value}

It is convenient to define the energy-momentum tensor in the vielbein basis (\ref{viel})
\begin{equation}
T^{ab} = R^{ab} - \ft12 \eta^{ab} R\,.
\end{equation}
We find $T^{ab}={\rm diag}\{\rho,p,p,\tilde p\}$, with
\begin{equation}
\rho=\fft{3 -4\alpha}{4\alpha \ell^2}\,,\qquad p= \fft{1}{4\alpha\ell^2}\,,\qquad
\tilde p = \fft{4\alpha-1}{4\alpha \ell^2}\,.
\end{equation}
The original $\alpha=\ft12$ case gives rise to matter with uniform pressure \cite{Godel:1949ga}.  The null-energy condition requires that
\begin{equation}
\rho + p = \fft{1-\alpha}{\alpha \ell^2}\ge 0\,,\qquad \rho + \tilde p = \fft{1}{2\alpha \ell^2}\ge 0\,,
\end{equation}
which is satisfied by $0< \alpha\le 1$.  As we shall see presently this implies that G\"odel metrics in general have naked CTCs in the framework of Einstein gravity.

\subsection{Metrics asymptotic to G$_\alpha$ }

We now consider deformations of G$_\alpha$ by introducing a function of two constants
\begin{equation}
f=1 + \fft{a}{r} - \fft{b}{r^2}\,,\label{f}
\end{equation}
and deform the metric (\ref{gvac}) to become
\begin{equation}
ds^2 = \ell^2 \Big(-(dt + r d\phi)^2 + \alpha r^2 f d\phi^2 + \fft{dr^2}{r^2 f} + dz^2\Big)\,.\label{deformed}
\end{equation}
It is straightforward to verify that the curvature tensors (\ref{ricci-curv}) remain unchanged.  This implies that the metric (\ref{deformed}) is locally the same as (\ref{ricci-curv}).  However, globally, the deformed metric (\ref{deformed}) is different from (\ref{gvac}). An important difference is that in the deformed metric (\ref{deformed}), the coordinate $\phi$ is periodic, namely
\begin{equation}
\Delta \phi = \fft{4\pi}{\sqrt{\alpha}\, r_0^2 f'(r_0)}\,,\qquad {\rm  with}\qquad f(r_0)=0\,.
\label{phip}
\end{equation}
This ensures that the metric is absent from a conical singularity at $r=r_0$.  After imposing this condition, the coordinate transformation that relates (\ref{gvac}) to (\ref{deformed}) breaks the scaling symmetry (\ref{scaling}) and hence the two metrics are not equivalent globally.

  To demonstrate this explicitly, we note that the parameter $a$ is trivial in that
it can be eliminated by the coordinate transformation $r\rightarrow r-\ft12a$, without altering the global structure.  The positive parameter $b$ can be set to $1$ without loss of generality, using the scaling $r\rightarrow \sqrt{b}\,r$, together with appropriate scalings of the rest coordinates.  Now let $r=\cosh\hat r$, $\phi=\hat \phi/\sqrt\alpha$, $t=\hat t-\hat \phi/\sqrt\alpha$, the metric (\ref{deformed}) with $a=0$ and $b=1$ becomes
\begin{equation}
ds^2 = \ell^2\Big(-  \big(d\hat t + \ft{2}{\sqrt{\alpha}}\,\sinh^2(\ft12 \hat r)\, d\hat \phi\big)^2 + \sinh^2\hat r\, d\hat \phi^2 + d\hat r^2 + dz^2\Big)\,.\label{godel2}
\end{equation}
On the other hand, we find that under the coordinate transformation
\setlength\arraycolsep{2pt} \begin{eqnarray}
&&r=\cosh \hat r + \cos\hat \phi\, \sinh \hat r\,,\qquad
r\phi =\fft1{\sqrt\alpha} \sin\hat\phi\,\sinh\hat r\,,\nonumber\\
&& \tan\big(\ft12\hat \phi + \ft12\sqrt\alpha\, (t - \hat t)\big) = e^{\hat r}
\tan(\ft12 \hat \phi)\,,\label{trans}
\end{eqnarray}
the metric (\ref{gvac}) becomes also precisely (\ref{godel2}).  (This coordinate transformation reduces to the one obtained in \cite{Godel:1949ga} for $\alpha=\ft12$.)  Thus it becomes clear that when $\Delta\hat\phi=2\pi$ is fixed, the scaling symmetry of the vacuum (\ref{gvac}) is broken by the coordinate transformation (\ref{trans}), and hence the two metrics are not globally equivalent.  An important consequence is that the metric (\ref{godel2}) has CTCs for $r> r_c$ with
\begin{equation}
\tanh(\ft12 r_c) =\sqrt{\alpha}\,.\label{vls}
\end{equation}
Here $r=r_c$ is the velocity of light surface (VLS) for which $g_{\hat\phi\hat\phi}=0$. We shall call the metric (\ref{deformed}) as the deformed G\"odel metric that is asymptotic to the G\"odel metric.  For general parameters $(a,b)$, there can be two VLS's between which $g_{\phi\phi}>0$. The global structure of the metric (\ref{deformed}), written in somewhat different parametrization, was analysed in \cite{Banados:2005da}.

The emerging of the CTCs in G\"odel metrics is a consequence of that $\alpha \le 1$. If one allows $\alpha>1$, equation (\ref{vls}) has no real solution for $r_c$, and the metrics do not have naked CTCs.  However, as we saw earlier that in the framework of Einstein gravity, $\alpha>1$ violates the null energy condition.  In higher-derivative gravity due to the $\alpha'$-correction of string theory, solutions with $\alpha>1$ were constructed in \cite{Barrow:1998wa}.  However, the theory, when treated on its own, involves inevitable ghost modes.

\subsection{Mass and angular momentum}

The general G\"odel metric has two Killing vectors
\begin{equation}
\xi_t = \fft{1}{\ell^2} \fft{\partial}{\partial t}\,,\qquad \xi_\phi = \fft{1}{\ell} \fft{\partial}{\partial \phi}\,.
\end{equation}
(The Killing symmetry in $z$ direction can be broken by the matter sector in some solutions.) Following the Wald formalism \cite{Wald:1993nt}, which computes the variation of the on-shell Hamiltonian $\delta {\cal H}$ associated with a Killing vector with respect to the integration constants of the solutions, we read off the associated conversed quantities by evaluating $\delta {\cal H}$ at asymptotic infinity, and find
\begin{equation}
M= \fft{\sqrt{\alpha}\,a}{16\pi}\Delta\phi\,,\qquad
J=\fft{\ell \sqrt{\alpha}\,b}{16\pi} \Delta \phi\,,
\end{equation}
where $\Delta\phi$ is given by (\ref{phip}).  Note that if one chooses a fixed period $\Delta\phi=2\pi$ instead, rather than given by (\ref{phip}), the solution will have naked singularity at $r=r_0$, for generic $\alpha$.  We have also set the convention $\int dz=1$.  For periodic $z$, this means period $\Delta z=1$; for real line $z$, this implies that the extensive quantities such as $M$ and $J$ are in fact uniform densities over the line $z$.

\subsection{Squashed 3-sphere $S^3_\alpha \times \mathbb T$}

In the G\"odel metrics, if we let $\ell^2 =-\tilde \ell^2<0$, the metric (\ref{deformed}) becomes
\begin{equation}
ds^2 = \tilde \ell^2 \Big((dz + r d\phi)^2 + \alpha h d\phi^2 + \fft{dr^2}{h} - dt^2\Big)\,,
\end{equation}
where we have swapped the role of $(t,z)$, and set, without loss of generality, $h=1-r^2$.  Let $r=\cos\theta$, we have
\begin{equation}
ds^2 = \tilde \ell^2 \Big((dz + \cos\theta d\phi)^2 + \alpha \sin^2\theta d\phi^2 +d\theta^2 - dt^2\Big)\,.\label{squashs3}
\end{equation}
This metric describes a direct product of time with a squashed 3-sphere, which we call $S_\alpha^3$.  When the squashing parameter $\alpha=1$, $S_\alpha^3$ becomes the round $S^3$, written as a $U(1)$ bundle over $S^2$.  The regularity of $S_\alpha^3$ requires that
\begin{equation}
\Delta\phi=\fft{2\pi}{\sqrt{\alpha}}\,,\qquad \Delta z = \fft{4\pi}{\sqrt{\alpha}}\,.
\end{equation}
The period $\Delta z$ can be divided by a natural number $n$ without introducing any singularity to the manifold, giving rise to $S_\alpha^3/\mathbb Z_n$.  (Such compact G\"odel universe was also considered in \cite{Israel:2004vv}.)

\section{G\"odel solutions from Lagrangian formalism}

As mentioned in the introduction, theories in literature associated with G\"odel universe (\ref{gvac}) or (\ref{deformed}) typically involve a matter energy-momentum tensor with unknown Lagrangian origin.  The known example in four dimensions is the Einstein-Maxwell theory with an axion and a negative cosmological constant \cite{Reboucas:1982hn}
\begin{equation}
{\cal L}=\sqrt{-g} \Big( R -2\Lambda- \ft12 (\partial\chi)^2 - \ft14 F^2)\,,\label{lag0}
\end{equation}
where $F=dA$ is the field strength. For the metric (\ref{gvac}), the solutions for matter fields are
\begin{equation}
A=\sqrt{2(1-\alpha)}\,\ell\, \sin(\fft{z}{\sqrt{\alpha}})\, (dt + r d\phi)\,,\qquad \chi =\fft{z}{\sqrt{\alpha}}\,,\qquad \ell^2 = -\fft{1}{2\Lambda}\,.
\end{equation}
In this case, the continuous shifting symmetry along the $z$-direction is broken to a discrete symmetry by the Maxwell potential $A$ that is periodic in $z$. (The axion $\chi$ field does not break this symmetry since only $d\chi$ appears in the theory.)  The solution is best described as G$_\alpha\times S^1$ rather than G$_\alpha\times \mathbb R$. A consequence is that G$_\alpha$ is not a solution to the three-dimensional massless sector in the Kaluza-Klein reduction of (\ref{lag0}) on $z$.  In this section, we shall construct more examples of Lagrangians that admit the G\"odel metrics of G$_\alpha \times \mathbb R$ as exact solutions.

\subsection{Einstein-Maxwell-Axion theory with a topological term}\label{sec3}

In addition to (\ref{lag0}), we introduce an additional topological term:
\begin{equation}
{\cal L} = \sqrt{-g} \left(R- 2\Lambda -\ft14 F^2 -\ft12\left(\partial \chi\right)^2 \right) +\ft18 \varepsilon^{\mu\nu\rho\sigma}\, \chi\,F_{\mu\nu} F_{\rho\sigma} \,, \label{eq23}
\end{equation}
where $F=dA$ is the field strength, $\varepsilon^{\mu\nu\rho\sigma}$ is the density of Levi-Civita tensor whose components are $\pm1, 0$. We choose the convention $\varepsilon^{0123}=1$. The axion, Maxwell and Einstein equations of motion are given by
\begin{eqnarray}
&&\partial_\mu \left(\sqrt{-g} \partial^\mu\chi\right) +\ft18 \varepsilon^{\mu\nu\rho\sigma} F_{\mu\nu} F_{\rho\sigma}=0 \,,\qquad \partial_\mu\left(\sqrt{-g} F^{\mu\nu} - \ft12 \chi  \varepsilon^{\mu\nu\rho\sigma} F_{\rho\sigma} \right) =0 \,,  \nonumber \\
&&R_{\mu\nu} -\frac{1}{2}g_{\mu\nu} R +g_{\mu\nu}\Lambda -\ft12(F_{\mu\rho}{F_{\nu}}^{\rho} -\ft14g_{\mu\nu}F^2) -\ft12(\partial_\mu\chi\partial_\mu\chi -\ft12 g_{\mu\nu}(\partial\chi)^2) =0\,. \label{eq24}
\end{eqnarray}
For the general G\"odel metric (\ref{deformed}) with (\ref{f}), we consider the following ansatz for the axion and Maxwell field
\begin{equation}
A = q r\, d\phi \,, \qquad  \chi = k z\,.\label{eq27}
\end{equation}
We find that the equations of motion are all satisfied provided that
\begin{equation}
k = \frac{1}{\sqrt{\alpha}},\quad \alpha= 1-\frac{q^2}{2 \ell^2},\quad \ell^2= -\frac{1}{2\Lambda}\,.\label{eq28}
\end{equation}
The general solution contains three integration constants, $(a,b,q)$. The reality condition requires that $|q|< \sqrt2\,\ell$. It follows that we have $0<\alpha\le 1$ and $k\ge 1$.  The original $\alpha=\ft12$ G\"odel metric corresponding to $q=\ell$.  The AdS$_3$ factor arises when $\alpha=1$, corresponding to turning off the Maxwell field.  In section 3.3, we consider the case with $\alpha <0$, for which the metric describes $S_\alpha^3\times \mathbb T$.

It is worth pointing out that in four dimensions, the axion $\chi$ is Hodge dual to a 2-form potential $B_{\sst{(2)}}$ with
\begin{equation}
G_{\sst{(3)}} =dB_{\sst{(2)}}= {*d\chi} + \ft12 A\wedge F\,.\label{dual}
\end{equation}
The Lagrangian (\ref{eq23}) is equivalent to
\begin{equation}
{\cal L} = \sqrt{-g} \Big(R - 2\Lambda - \ft14 F^2 - \ft1{12} G_{\sst{(3)}}^2\Big)\,.
\end{equation}
For the G\"odel solutions we have $B_{\sst{(2)}} = r dt\wedge d\phi$.  The 3-form field strength $G_{\sst{(3)}}$ is suggestive of string theory, which we shall discuss in section 5.

\subsection{Einstein-Proca-Axion theory}

In this subsection, we replace the previous Maxwell field by a Proca field of mass $\mu$, with the Lagrangian
\begin{equation}
{\cal L}_2 = \sqrt{-g} \left(R- 2\Lambda -\ft14 F^2 -\ft12\mu^2 A^2 -\ft12\left(\partial \chi\right)^2 \right) \,. \label{eq31}
\end{equation}
The equations of motion are
\setlength\arraycolsep{2pt} \begin{eqnarray}
&&\Box \chi =0\,,\qquad \nabla_\mu F^{\mu\nu} - \mu^2 A^\nu =0\,,\cr
&&R_{\mu\nu} -\ft{1}{2}g_{\mu\nu} R +g_{\mu\nu}\Lambda -\ft{1}{2}\left(F_{\mu\rho}{F_{\nu}}^{\rho} -\ft{1}{4}g_{\mu\nu}F^2\right) -\ft12\mu^2\left(A_\mu A_\nu -\ft{1}{2}g_{\mu\nu}A^2 \right) \cr
&&\quad -\ft{1}{2}\left(\partial_\mu\chi\partial_\mu\chi -\ft{1}{2}g_{\mu\nu}(\partial\chi)^2\right) =0\,. \label{eq32}
\end{eqnarray}
(There should be no confusion between the Proca mass $\mu$ and the spacetime indices.) The metric ansatz is given in (\ref{deformed}).  We consider the following ansatz for $A$ and $\chi$:
\begin{equation}
A= q (dt + r d\phi) \,, \qquad  \chi = z\,.
\end{equation}
Substituting these into the equations of motion, we find
\begin{equation}
\mu= \frac{1}{\ell\sqrt{\alpha}}, \quad \Lambda= \frac{3q^2-2\ell^2}{4\ell^2 (\ell^2-q^2)} , \quad \alpha = 1- \frac{q^2}{\ell^2} \,.\label{eq36}
\end{equation}
Note that all the constants except for $(a,b)$ appearing in the solution are fixed by the coupling constants of the theory, namely $(\Lambda, \mu)$.  It follows that unlike in the earlier EMA theory, the general solution involves only two integration constants. The original $\alpha=\ft12$ G\"odel metric corresponds to taking $q=\ell/\sqrt2$.

\subsection{The embedding of squashed 3-sphere}

In the embedding of the G\"odel metric in both EMA and EPA theories discussed above, the cosmological constant $\Lambda$ is negative.  When it is positive, the metric G$_\alpha\times \mathbb R$ becomes $S_\alpha^3\times \mathbb T$, as in (\ref{squashs3}).  For the EMA theory, we have
\begin{equation}
A = q \cos\theta\, d\phi \,, \qquad  \chi = \fft{t}{\sqrt{\alpha}}\,, \qquad \tilde \ell^2= \fft{1}{2\Lambda}\,,\qquad \alpha= 1+\fft{q^2}{2 \tilde \ell^2}\,.
\end{equation}
For the EPA theory, we have
\begin{equation}
A=q (dz + \cos\theta\, d\phi) \,, \quad  \chi = t\,,\quad
\mu^2= -\frac{1}{\tilde \ell^2\alpha}, \quad \Lambda= \frac{3q^2+2\tilde\ell^2}{4\tilde \ell^2 (\tilde \ell^2+q^2)} , \quad \alpha = 1+\frac{q^2}{\tilde \ell^2} \,.
\end{equation}
Thus we see that the embedding of the $S_\alpha^3$ in EPA theory requires a tachyonic vector with $\mu^2<0$, while in the EMA theory, no exotic matter is required.

\subsection{Generalizing to higher dimensions}

In this section, we generalize the G\"odel universe to higher dimensions by considering G$_\alpha\times \mathbb{R}^n$, namely
\begin{equation}
ds^2 = \ell^2 \Big(-(dt + r d\phi)^2 + \alpha r^2 f d\phi^2 + \fft{dr^2}{r^2 f} + dz^idz^i\Big)\,,\qquad i=1,2,\ldots,n.\label{deformed2}
\end{equation}
The $\alpha=\ft12$ solution can be still solved by (\ref{pfluid}), but with $u^\mu=(\ell^{-2},0,\ldots,0)$.

In order for the metrics to be solutions of some Lagrangians, we can replace the axion $\chi$ in the previous subsections by a $(n-1)$-form potential $B_{(n-1)}$ with the field strength $G_{(n)}=dB_{(n-1)}$.  The Lagrangian (\ref{eq23}) becomes
\begin{equation}
{\cal L} = \sqrt{-g} \left[R- 2\Lambda -\ft14 F^2 -\ft1{2\,n!} G_{(n-1)}^2 \right] +\ft1{8\,(n-1)!} \varepsilon^{\mu\nu\rho\sigma\alpha_1\cdots\alpha_{n-1}}\, B_{\alpha_1\cdots\alpha_{n-1}}\,F_{\mu\nu} F_{\rho\sigma} \,.
\end{equation}
(This should not be confused with dualizing $d\chi$ to the 3-form field strength in four dimensions, discussed in the end of subsection 3.1.) The axion ansatz (\ref{eq27}) is replaced by
\begin{equation}
G_{(n)}= k\, dz_1\wedge\cdots dz_n\,.\label{gn}
\end{equation}
The Lagrangian (\ref{eq31}) is now replaced by
\begin{equation}
{\cal L}_2 = \sqrt{-g} \left(R- 2\Lambda -\ft14 F^2 -\ft12\mu^2 A^2 -\ft1{2\,n!} G_{(n)}^2 \right) \,.
\end{equation}
The corresponding ansatz for $G_{(n)}$ is given by (\ref{gn}) with $k=1$.

\subsection{Effective three-dimensional theories}

The non-trivial part of the G\"odel universe is the three-dimensional metric G$_\alpha$. For the solutions in subsections 3.1 and 3.2, the Killing symmetry in $z$ direction is maintained by the matter fields.  We can thus perform dimensional reduction on the coordinate $z$.  The EMA theory becomes
\begin{equation}
{\cal L} = \sqrt{-g} \left(R- 2\Lambda_{\rm eff} -\ft14 F^2 \right) +\ft14 \lambda_{\rm eff} \,\varepsilon^{\mu\nu\rho} A_\mu F_{\nu\rho} \,,
\end{equation}
In this case, the three-dimensional G$_\alpha$ metric is now supported by
\begin{equation}
A=q r d\phi\,,\qquad \alpha = 1 - \fft{q^2}{2\ell^2}\,,\qquad \Lambda_{\rm eff} = \fft{q^2-\ell^2}{2\ell^2(2\ell^2-q^2)}\,,\qquad \lambda_{\rm eff}^2 = \fft{2}{2\ell^2 - q^2}\,.
\end{equation}
The G$_\alpha$ metric of this theory was constructed in \cite{Banados:2005da}, where the global structure of G$_\alpha$ was discussed. Under the Kaluza-Klein reduction, the EPA theory becomes
\begin{equation}
{\cal L} = \sqrt{-g} \left(R- 2\Lambda_{\rm eff} -\ft14 F^2 -\ft12\mu^2 A^2\right) \,.
\end{equation}
In this case, the G$_\alpha$ metric is supported by
\begin{equation}
A= q (dt + r d\phi)\,,\qquad \mu= \frac{1}{\ell\sqrt{\alpha}}, \qquad  \alpha = 1- \frac{q^2}{\ell^2} \,,\qquad
\Lambda_{\rm eff}= \frac{2q^2-\ell^2}{4\ell^2 (\ell^2-q^2)}\,.
\end{equation}
In both theories, the free parameters of the solutions are $(a,b)$ of function $f$ (\ref{f}), whilst $q$ and hence $\alpha$ are fixed by the coupling constants of the theories. In the above dimensional reductions, we have performed further consistent truncations to subset of fields that are relevant to the G$_\alpha$ metrics.
Note that the solution at the beginning of this section involves the $z$-dependent $A$, and hence it cannot be reduced to the three-dimensional massless sector.

\section{Black holes from double Wick rotations}

\subsection{Type I}

As was discussed in \cite{Banados:2005da}, the metrics G$_\alpha$ can describe black holes in three dimensions after double Wick rotations
\begin{equation}
t\rightarrow {\rm i} t\,,\qquad \phi\rightarrow {\rm i} \phi\,.
\end{equation}
The general metric (\ref{deformed}) now becomes
\begin{equation}
ds^2 = \ell^2 \Big((dt + r d\phi)^2 - \alpha r^2 \tilde f d\phi^2 + \fft{dr^2}{r^2 \tilde f} + dz^2\Big)\,,\label{bhmetric}
\end{equation}
with the function $\tilde f$ now given by
\begin{equation}
\tilde f=1-\fft{a}{r} - \fft{b}{r^2}\,.
\end{equation}
For the EMA theory, we find that the matter fields are given by
\begin{equation}
A = q r\, d\phi \,, \quad  \chi =\fft{z}{\sqrt{\alpha}}\,,\quad\hbox{with}\quad
\ell^2= -\frac{1}{2\Lambda},\quad \alpha= 1+\frac{q^2}{2 \ell^2}\ge 1\,.
\end{equation}
For the EPA theory, we have
\begin{equation}
A= q (d\phi + r dt) \,, \quad  \chi = z\,,\quad\hbox{with}\quad
\mu= \frac{1}{\ell\sqrt{\alpha}}, \quad \Lambda= \frac{3q^2+2\ell^2}{4\ell^2 (\ell^2+q^2)} , \quad \alpha = 1+ \frac{q^2}{\ell^2}\ge 1 \,.
\end{equation}

Thermodynamics of three-dimensional black holes was studied in \cite{Banados:2005da}.  Here we would like to derive the first law in our context and notations.  New subtlety emerges in the EMA theory, where the parameter $q$ is an integration constant. For simplicity, we shall set $\ell=1$ for the following discussions.  We also assume that the coordinate $\phi$ is periodic with $\Delta\phi=2\pi$. Thus the solution describes a rotating metric.  The null-Killing vector on the horizon $r=r_0$ with $f(r_0)=0$ is given by
\begin{equation}
\xi=\fft{\partial}{\partial t} - \Omega_+ \fft{\partial}{\partial \phi}\,,\qquad \Omega_+=\fft{1}{r_0}\,.
\end{equation}
It is straightforward to verify that the surface gravity and hence the temperature are given by
\begin{equation}
\kappa = \fft{\sqrt{\alpha} r_0}{4\pi} \tilde f'(r_0)\,,\qquad T= \fft{\kappa}{2\pi}\,.
\end{equation}
The mass and angular momentum can be read off from the Wald formalism, given by
\begin{equation}
M=\ft18 \sqrt{\alpha}\, a\,,\qquad J=\ft18 \sqrt{\alpha}\, b\,.
\end{equation}
Two situations emerge at this stage.  For black holes of the EPA theory or the effective theories in three dimensions, the parameter $q$ and hence $\alpha$ are fixed constants.  In these cases, the first law of black hole thermodynamics reads
\begin{equation}
dM=T dS + \Omega_+ dJ\,.
\end{equation}
In the EMA theory; on the other hand, the parameter $q$ is an integration constant, and hence it can be varied and should be involved in the first law.  To complete the first law involving the parameter $q$, we first note that the electric charge of the Maxwell field vanishes, namely
\begin{equation}
\int {*F} + d\chi \wedge A=0\,.
\end{equation}
(In \cite{Banados:2005da}, an electric charge associated with pure gauge transformation of $A$ was introduced. We shall not consider this here.) The linear charge density of the axion field on the other hand is non-vanishing
\begin{equation}
Q_\chi =\ft18\int d\chi = \fft1{8\sqrt{\alpha}}\,.\label{qchi}
\end{equation}
The corresponding thermodynamical potential can be read off from the 2-form potential $B_{\sst{(2)}}$ that is Hodge dual to the axion, as in (\ref{dual}).  It is given by
\begin{equation}
\Phi_\chi=r_0\,.\label{axionp}
\end{equation}
We find the first law reads
\begin{equation}
dM = T dS + \Omega_+ dJ + \Phi_\chi d(\alpha Q_\chi)\,.
\end{equation}
It is puzzling that an extra factor $\alpha$ is needed for the completion of the first law above.

\subsection{Type II}

In this interpretation,  we switch $t$ and $\phi$ in (\ref{bhmetric}) and write the metric as
\begin{equation}
ds^2 = \ell^2 \Big((d\phi + (r-r_0) dt)^2 - \alpha r^2 \tilde f dt^2 + \fft{dr^2}{r^2 \tilde f} + dz^2\Big)\,.\label{bhmetric2}
\end{equation}
Note that we also made a coordinate transformation so that the null Killing vector at the degenerate surface $r=r_0$ with $\tilde f(r_0)=0$  is $\xi=\partial_t$.  In other words, the metric is non-rotating on the horizon. The temperature is given by
\begin{equation}
T=\fft{\sqrt{\alpha} r_0^2 \tilde f'(r_0)}{4\pi}\,.
\end{equation}
The solution has no CTCs since $g_{\phi\phi}=\ell^2$ and further more $g_{tt}>0$ for $r>r_0$, and hence $t$ is globally defined outside the horizon.  Note that in this case, the entropy is a constant since the radius of the $\phi$ circle is constant.  We can also show, using the Wald formalism that the mass and angular momentum both vanish.  The solution can be viewed as thermalized vacuum. In the EMA theory, $q$ is an integration constant, which leads to non-zero electric charge and potential, give by
\begin{equation}
Q_A= \fft{1}{16\pi}\int {*F} + d\chi \wedge A=\fft{q}{16\pi\sqrt{\alpha}} \int d\phi dz = \fft{q}{16\pi\sqrt{\alpha}}\Delta\phi\,,\qquad \Phi_A=q r_0\,.
\end{equation}
The axion charge and its thermodynamical potential are given by (\ref{qchi}) and (\ref{axionp}).  This leads to the first law of black hole ``thermodynamics''
\begin{equation}
\Phi_A dQ_A + \Phi_\chi dQ_\chi=0\,,
\end{equation}
provided that $\Delta\phi=\pi$.

\section{Embedding in string theory}

\subsection{Freedman-Schwarz model}
In section 3 we constructed some ad hoc theories that admit G\"odel metrics as exact solutions. The Maxwell and axion fields are common occurrence in supergravities, indicating that there may exist an exact embedding of G\"odel universe in supergravity and hence in string theory.  In this section, we consider Freedman-Schwarz $SU(2)\times SU(2)$ gauged supergravity whose bosonic sector consists of the metric, a dilaton $\varphi$, an axion and two $SU(2)$ Yang-Mills fields. After truncating to the $U(1)^2$ subsector, the corresponding Lagrangian is
\setlength\arraycolsep{2pt} \begin{eqnarray}
{\cal L} &=& \sqrt{-g} \Big(R - \ft12 (\partial \varphi)^2 - \ft12 e^{2\varphi} (\partial \chi)^2 + 2 (g_1^2 + g_2^2) e^{\varphi}- \ft14 e^{-\varphi} (F_1^2 + F_2^2)\Big)\cr
&&+\ft18 \varepsilon^{\mu\nu\rho\sigma}\, \chi\,(F_{1\,\mu\nu} F_{1\,\rho\sigma} + F_{2\,\mu\nu} F_{2\,\rho\sigma})\,,
\end{eqnarray}
where $(g_1,g_2)$ are the gauge coupling constants of the two $SU(2)$ Yang-Mills fields.
The theory admits the general deformed G\"odel metric (\ref{deformed}) with the matter fields given by
\begin{equation}
A_i=q_i r d\phi\,,\qquad \chi=\fft{z}{\sqrt{\alpha}}\,,\qquad \varphi=0\,,
\end{equation}
with the parameters
\begin{equation}
\ell^2 = \fft{1}{2(g_1^2 + g_2^2)}\,,\qquad \alpha= 1 - (g_1^2 + g_2^2) (q_1^2 + q_2^2)\,.\label{ellalpha}
\end{equation}

\subsection{G\"odel universe from string theory}

Freedman-Schwarz model can be obtained from the Kaluza-Klein reduction on $S^3\times S^3$ \cite{Chamseddine:1997mc,Cvetic:1999au}.  The relevant part of the effective Lagrangian of strings in ten dimensions is
\begin{equation}
{\cal L}_{10}=\sqrt{-g} \Big( R - \ft12 (\partial \Phi)^2 -\ft1{12} e^{-\Phi} F_{\sst{(3)}}^2\Big)\,,
\end{equation}
where $F_{\sst{(3)}}$ can be either NS-NS or R-R fields. Following the reduction ansatz given in \cite{Cvetic:1999au}, we find that the ten-dimensional solution is given by $\Phi=0$, together with
\setlength\arraycolsep{2pt} \begin{eqnarray}
ds_{10}^2 &=& \fft{1}{g_1^2 + g_2^2} \Big(-(dt + r d\phi)^2 + \alpha r^2 f\, d\phi^2 + \fft{dr^2}{r^2f} + dz^2\Big)\nonumber\\
&&+ \fft{1}{g_1^2} \Big( (d\psi_1 + \cos\theta_1\, d\phi_1 + g_1 q_1 r d\phi)^2 + d\theta_1^2 + \sin^2\theta_1\,d\phi_1^2\Big) \nonumber\\
&&+ \fft{1}{g_2^2} \Big( (d\psi_2 + \cos\theta_2\, d\phi_2 + g_2 q_2 r d\phi)^2 + d\theta_2^2 + \sin^2\theta_2\,d\phi_2^2\Big)\,,\\
F_{\sst{(3)}} &=& \fft{1}{g_1^2 + g_2^2} dt\wedge dr\wedge d\phi - \fft{\sin\theta_1}{g_1^2} d \theta_1\wedge d\phi_1\wedge
(d\psi_1 + \cos\theta_1\,d\phi_1 + g_1 q_1 r d\phi)\nonumber\\
&& - \fft{\sin\theta_2}{g_2^2} d\theta_2\wedge d\phi_2\wedge
(d\psi_2 + \cos\theta_2\,d\phi_2 + g_2 q_2 r d\phi)\nonumber\\
&& -\fft{q_1}{g_1} dr\wedge d\phi \wedge (d\psi_1 + \cos\theta_1\, d\phi_1)
-\fft{q_2}{g_2} dr\wedge d\phi \wedge (d\psi_2 + \cos\theta_2\, d\phi_2)\,.\label{10dsol}
\end{eqnarray}
Here $\alpha$ is again given by (\ref{ellalpha}).
The solution involves both electric string and magnetic fivebrane/fivebrane charges, given by
\setlength\arraycolsep{2pt} \begin{eqnarray}
\hbox{electric}:&& Q_1\sim \int {*F}_{\sst{(3)}} \sim \fft{1}{\sqrt{\alpha} g_1^3 g_2^3}\,,\cr
\hbox{magnetic}:&& Q_{5/5}\sim \int F_{\sst{(3)}} \sim \fft{1}{g_1^2} + \fft1{g_2^2}\,.
\end{eqnarray}
These can be either all NS-NS charges or R-R charges, and the latter corresponds to the D1/D5/D5 configuration. When $q_1=0=q_2$, the metric becomes AdS$_3\times S^3\times S^3\times \mathbb R$, which is the decoupling limit of the string/fivebrane/fivebrane configuration \cite{Cowdall:1998bu}.  The rotations associated with parameters $(q_1,q_2)$ turn the AdS$_3$ into the G$_\alpha$.  We thus expect that there should be a rotating string/fivebrane/fivebrane configuration whose decoupling limit gives rise to our ten-dimensional solution (\ref{10dsol}).  If we set either $g_1=0$ or $g_2=0$, but not both, the associated $S^3$ is flatten to become $\mathbb R^3$.  The metric configuration becomes $G_\alpha\times S^3\times \mathbb R^4$.  The heterotic string solution of $G_\alpha \times S^3\times K_3$ was first constructed in \cite{Israel:2003cx}.

To study the global structure, we first denote $r_0$ as the largest root of $f(r)$.  Shifting the coordinates as
\begin{equation}
t\rightarrow t - r_0\phi\,,\qquad \psi_i \rightarrow \psi_i - g_i q_i r_0\phi\,,
\end{equation}
we find that the metric is singular at $r=r_0$, where the degenerate Killing vector is purely spatial $\xi=\partial_\phi$. The absence of a conical singularity requires that
\begin{equation}
\Delta \phi = \fft{4\pi}{\sqrt{\alpha} r_0^2 f'(r_0)}\,.
\end{equation}
Thus in this system, there are three periodic coordinates $\phi$, and $(\psi_1,\psi_2)$, with $\Delta\psi_1=4\pi=\Delta \psi_2$. The coordinate $t$ on the other hand is not required to be periodic.  The analysis of CTCs in ten dimensions becomes more subtle.  Note that we have
\begin{equation}
g_{\phi\phi} = \fft{\alpha r_0^2 f'(r_0)}{g_1^2 + g_2^2} (r-r_0)\ge 0\,,
\end{equation}
for the region $r\ge r_0$; however, naked CTCs still exist.  One way to see this is to consider the general periodic Killing vector
\begin{equation}
\xi=\beta \fft{\partial}{\partial\phi} + \gamma_1 \fft{\partial}{\partial \psi_1} +
\gamma_2 \fft{\partial}{\partial \psi_2}\,.
\end{equation}
The absence of naked CTCs requires that $\xi^2\ge 0$ for all real $(\beta,\gamma_1,\gamma_2)$ in the $r\ge r_0$ region.  This can be easily established not true.  Negative modes arise for large enough $r$.

   A simpler way to see that naked CTCs exist is the follows.  Let $r=r_*$ such that
$r_*^2(\alpha f(r_*)-1)<0$,  which is always achievable since $0<\alpha<1$. Now making a coordinate shifting $\psi_i\rightarrow \psi_i - g_i q_i r_*\phi$, then we have $g_{\phi\phi}(r_*)=r_*^2(\alpha f(r_*)-1)<0$.

\subsection{AdS$_3\times S^3$ bundle over $S_\alpha^3$}

We now consider the case with negative $g_1^2=-\hat g_1^2$ and $\hat g_1^2 - g_2^2>0$.  Performing some appropriate analytical continuation of the coordinates on the solution (\ref{10dsol}) and then dropping the hat symbol, we have
\setlength\arraycolsep{2pt} \begin{eqnarray}
ds_{10}^2 &=& \fft{1}{g_1^2 - g_2^2} \Big((d\psi + \cos\theta\, d\phi)^2 + \alpha \sin^2\theta\, d\phi^2 + d\theta^2+ dz^2\Big)\nonumber\\
&&+ \fft{1}{g_1^2} \Big( (d\psi_1 + \rho dt + g_1 q_1 \cos\theta\, d\phi)^2 +\fft{d\rho^2}{\rho^2+1} -(\rho^2+1)\,dt^2\Big) \nonumber\\
&&+ \fft{1}{g_2^2} \Big( (d\psi_2 + \cos\theta_2\, d\phi_2 + g_2 q_2 \cos\theta\, d\phi)^2 + d\theta_2^2 + \sin^2\theta_2\,d\phi_2^2\Big)\\
F_{\sst{(3)}} &=& -\fft{1}{g_1^2 - g_2^2} d\psi\wedge d\cos\theta\wedge d\phi + \fft{1}{g_1^2} d\rho\wedge dt\wedge
(d\psi_1 + \rho\,dt + g_1 q_1 \cos\theta\, d\phi)\nonumber\\
&& - \fft{\sin\theta_2}{g_2^2} d\theta_2\wedge d\phi_2\wedge
(d\psi_2 + \cos\theta_2\,d\phi_2 + g_2 q_2 \cos\theta\, d\phi)\nonumber\\
&& -\fft{q_1}{g_1} d\cos\theta\wedge d\phi \wedge (d\psi_1 + \rho dt)
-\fft{q_2}{g_2} d\cos\theta\wedge d\phi \wedge (d\psi_2 + \cos\theta_2\, d\phi_2)\,,
\end{eqnarray}
where $\alpha=1 + (g_1^2-g_2^2)(q_1^2 + q_2^2)$.  The solution describes a direct production of a line of coordinate $z$ and a nine-dimensional metric of an AdS$_3\times S^3$ bundle over squashed 3-sphere $S_\alpha^3$.  Again the configuration involves both electric string and magnetic fivebrane/fivebrane charges
\setlength\arraycolsep{2pt} \begin{eqnarray}
\hbox{electric}:&& Q_1\sim\fft{g_1}{\sqrt{\alpha}\,g_2^2(g_1^2-g_2^2)^2}\,,\nonumber\\
\hbox{magnetic}:&& Q_{5/5} \sim \fft{1}{\alpha\, (g_1^2 - g_2^2)} + \fft1{g_2^2}\,.
\end{eqnarray}
Note that $\Delta\psi\sim \Delta\phi\sim 1/\sqrt{\alpha}$.
When $q_1=0=q_2$, the metric is again AdS$_3\times S^3\times S^3$, equivalent to the previous static case.  For non-vanishing $q_i$'s, the brane configuration is not clear and it deserves further study.  Interestingly, the limit of $g_1=g_2$ leads to the well-known AdS$_3\times S^3\times \mathbb R^4$ vacuum of string theory, and the limit $g_2=0$ gives rise to AdS$_3\times S_\alpha^3\times \mathbb R^4$.

\section{Conclusions}

Four-dimensional G\"odel metrics of G$_\alpha\times \mathbb{R}$ are perhaps the simplest solutions that exhibit naked CTCs with no globally spatial-like Cauchy horizon.  In this paper, we showed that the G\"odel metrics could arise as exact solutions in Lagrangian formalism.  We constructed EMA and EPA theories that admit G\"odel solutions.  We also showed that G\"odel universe could emerge from Freedman-Schwarz $SU(2)\times SU(2)$ gauge supergravity.  This allows us to give exact embeddings of the G\"odel metrics in string theories.  The ten-dimensional solution describes a direct product of a line and an $S^3\times S^3$ bundle over G$_\alpha$. Classically, we find that naked CTCs persist in higher dimensions. (In \cite{Israel:2003cx}, string quantization was performed on G$_\alpha\times S^3\times K_3$ and it was demonstrated that CTCs can resolved by the quantum effects.) For some appropriate choice of parameters, the nine-dimensional metric can describe an AdS$_3\times S^3$ bundle over a squashed 3-sphere $S_\alpha^3$, in which case, there is no CTC.  In the suitable limit, the solution becomes the supersymmetric AdS$_3\times S^3\times \mathbb R^4$ vacuum.

The scaling symmetry of the metric (\ref{gvac}) resembles that of the anti-de Sitter spacetimes.  This is suggestive that there may exist a boundary field theory at the $r\rightarrow \infty$ boundary of G\"odel universe. The exact embedding of the G\"odel metrics in string theory, as the decoupling limit of the rotating D1/D5/D5 intersection, provides a tool of investigating the boundary field theory in the context of string theory.

\section*{Acknowlegement}

S.-L.L. and H.W. are supported in part by NSFC under Grants NO. 11575022 and NO. 11175016. X.-H.F. and H.L. are supported in part by NSFC grants NO. 11175269, NO. 11475024 and NO. 11235003.

redpajama_set_name: RedPajamaArXiv


text:
Q: Average between two columns in mysql that are date not timestamp Alright so here it is. I need to figure out the average amount of days between two columns.
Column 1 is recieved_date and column 2 is fix_date
Just want to know how to take the two dates find the difference in days, do that for every row and pop out a number stating the average amount of days it takes to fix something.
Tried to find it online but every time I find something like it, they have two specific dates. I need the entire columns averaged.

A: You can use the TIMESTAMPDIFF function both for dates and datetime.
See Mysql average time between visits

A: Add a group by and some other columns to this and it should do the trick:
select
  avg(fix_period)
from
(
select
  datediff(fix_date, received_date) as fix_period
  from some_table
) as a
;

redpajama_set_name: RedPajamaStackExchange


text:
Keep up with the rapidly evolving COVID-19 situation.
Public Health & Guidelines
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For Front-Line Workers
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What is the role of shelter hospitals in the current COVID-19 Pandemic?
April 30, 2020 May 1, 2020 by mranalidengre
Fangcang shelter hospitals can be a strong component of the national response for handling the current COVID-19 pandemic as well as for any future epidemics and public health emergencies.
Chen, S. et al. Fangcang shelter hospitals: a novel concept for responding to public health emergencies. The Lancet (2020). https://doi.org/10.1016/S0140-6736(20)30744-3
Fangcang shelter hospitals are a novel public health concept that was introduced for the first time in China in February 2020 in response to the COVID-19 outbreak. Fangcang hospitals are large-scale, temporary hospitals. They are made by converting existing infrastructure, such as stadiums and exhibition centers, into healthcare facilities in order to isolate patients with mild to moderate symptoms of the disease. These hospitals also provide medical care, disease monitoring, food, shelter, and social activities. These hospitals have three key characteristics. The first is rapid construction: they can be built quickly because they are based inside an existing physical infrastructure. Secondly, they provide a massive scale – the ability to convert existing large-scale public venues to serve hospital functions provides a huge leverage to increase healthcare capacity. The third characteristic is the low cost of building and running these hospitals, as converting existing venues prevents costly construction of new physical infrastructure. Furthermore, the Fangcang hospitals serve five essential functions: isolation of patients with mild to moderate symptoms, triage, providing basic medical care, frequent monitoring and rapid referral to traditional hospital in case of severe or critical disease, and essential living and social engagement to promote patient recovery and alleviate anxiety that the pandemic and isolation could cause. Fangcang hospitals can be a national standard of care during public health emergencies to bridge a gap until the capacity for mass treatment can be established. These Fangcang shelter hospitals can be rapidly established and can provide space for a large number of hospital beds and appropriate care for patients who do not have severe or critical disease.
Summary by: Parth Patel
Impact of mass testing facilities and resolution of COVID-19 pandemic
What is the role of TeleHealth in COVID-19?


text:
Meet the young lady who knows something about my wife which I didn't know
'Sir, here are the two coffees. I have marked one with K. That's for ma'am'
I was at the Krispy Kreme outlet at Bandra's Turner Road on Sunday morning. K and I were running late for an engagement. I had wanted to call in for coffees at home but K wanted the Krispy Kreme cappuccino.
'It makes me feel good,' she said.
Unlike Starbucks, Krispy Kreme doesn't deliver coffee on Swiggy, an app we often use to call in for coffee and other stuff. So we took a rick and stopped Krispy Kreme on the way to our meeting. K waited in the rick while I went in and placed our order of two cappuccinos to go.
I was sleepy and also anxious about making it to our engagement in time and I didn't pay much attention to what was happening at the counter after I placed my order.
The girl's comment, when the coffees were ready, snapped me back to attention. I hadn't specified who I wanted the second coffee for after all, let alone their preferences!
'That's madam's coffee? What's the difference?' I asked.
'She likes her coffee light sir,' she said.
'She does?' I replied, flummoxed and collected our cappuccinos.
I left with our coffees very impressed. K and I are regulars at this outlet. We don't always come here together. I usually come here to pick a coffee on the way if I have a morning meeting.
The staff is alway smiling and cheerful when I come here. Including the young girl who served us the coffee today whom I had seen here before too.
I had bothered to ask her her name in the past. Yet she knew enough of me to know that I was picking the second coffee for K and also what type of coffee she liked.
I requested K to ask her her the next time she went there.
K did go to Krispy Kreme in the evening for another cappuccino and now that I know the young girl's name , "thank you for the coffee and the smiles Salma and for teaching me what it means to 'treasure the individual in front of you' ".
Have a lovely week ahead guys.
Aadil Desai said…
That's really sweet of her to remember the choices, had a similar experience in a small boutique hotel in Baroda where the staff always remembeed my tea preference and got it just the way I like it. In a big mug instead of the small cup!!!
I feel fortunate to come across such people. Syliva at candies who knows our orders by heart is another
nprashant nayakanti said…
Keep up the wonderful work


text:
class Location
    attr_accessor :lat, :long

    def initialize(lat, long)
        @lat = lat
        @long = long
    end
end

# An application
class Web
    attr_accessor :name, :url

    def initialize(name, url)
        @name = name
        @url = url
    end
end

# An simple author element with some description
class Author
    attr_accessor :title, :email, :categories, :locations, :origin

    def initialize(title, email, categories, locations, origin)
        @title = title
        @email = email
        @categories = categories
        @locations = locations
        @origin = origin
    end
end

# An general news entry
class News
    attr_accessor :config, :inline_config, :tags, :receiver, :resources, :profile_image, :read, :source, :author, :meta, :send_date, :read_date, :expires, :price, :rating, :content, :question, :version, :coffee_time, :profile_uri, :captcha, :payload

    def initialize(config, inline_config, tags, receiver, resources, profile_image, read, source, author, meta, send_date, read_date, expires, price, rating, content, question, version, coffee_time, profile_uri, captcha, payload)
        @config = config
        @inline_config = inline_config
        @tags = tags
        @receiver = receiver
        @resources = resources
        @profile_image = profile_image
        @read = read
        @source = source
        @author = author
        @meta = meta
        @send_date = send_date
        @read_date = read_date
        @expires = expires
        @price = price
        @rating = rating
        @content = content
        @question = question
        @version = version
        @coffee_time = coffee_time
        @profile_uri = profile_uri
        @captcha = captcha
        @payload = payload
    end
end

redpajama_set_name: RedPajamaGithub


text:
Faïza Guène (född 7 juni 1985 i Bobigny, en förort till Paris) är en fransk författare och filmare med algerisk bakgrund.

Biografi
Som tonåring deltog Guène i en skrivarkurs och läraren lämnade hennes manus vidare till sin syster, som var förlagsredaktör. Debutromanen Kiffe Kiffe i morgon (original Kiffe kiffe demain) utkom 2004 och blev en succé. Faïza Guène sågs som en representant för Förortsfrankrike, och en del kritik har framförts mot att hon skrivit på förortsslang i stället för på klassisk franska.

I romanen "Kiffe Kiffe i morgon" berättar den 15-åriga Doria om sitt liv i förorten. För författaren var det viktigt att visa vardagen i förorten, inte bara våld och kriminalitet som tidningarna skriver om.

Guène var en av de 39 arabiska författare under 40 år som valdes ut till antologin Beirut 39, huvudprojektet när Beirut var Unescos bokhuvudstad 2009.

Filmografi
Rumeurs, 2002 (kortfilm)
Mémoires du 17 octobre 61, 2002 (dokumentärfilm om Massakern i Paris 1961)
Rien que des mots, 2004 (kortfilm)

Bibliografi
Kiffe kiffe demain. 2004. Utgiven på svenska 2006 av Norstedts förlag, svensk titel: Kiffe kiffe imorgon. Översättning av Lotta Riad.
Du rêve pour les oufs. 2006. Utgiven på svenska 2008 av Norstedts förlag, svensk titel: Drömmar för dårar. Översättning av Lotta Riad.
Les gens du Balto. 2008. Utgiven på svenska 2010 av Norstedts förlag, svensk titel: Sista beställningen på Balto. Översättning av Lotta Riad.
Un homme ça ne pleure pas. 2015. Utgiven på svenska 2015 av Nordstedts förlag, svensk titel: En riktig man gråter inte. Översättning av Lotta Riad.

Antologi

Priser och utmärkelser
 Peter Pan-priset 2007

Referenser

Externa länkar

Franska författare
Franskspråkiga författare
Kvinnor
Födda 1985
Levande personer
Personer från Bobigny

redpajama_set_name: RedPajamaWikipedia


This is the mechanical gun you have been waiting for! The Infamous Edition Planet Eclipse Gmek is now in stock!
This means BOTH the mechanical slide frame and electronic frame are included so you can swap back and forth!
The reliability of a modern marker with the nostalgic feel of a classic mechanical gun. Now you can have the best of both worlds with an Infamous Twist. The LE Infamous GMeks are now shipping!


Gurgling tums, wind and flatulence can affect all pets at various times and some pets are especially prone to digestive upsets of this nature. This supplement contains calming herbs like ginger and valerian, rhubarb and peppermint to aid digestion and slippery elm to soothe and comfort.
Can be given long term to susceptible pets or short term to settle the digestion before an event and for those that suffer from motion sickness.


If a version property would be added to the database it can be checked from code or in the Administrator client or in the Catalog. It can be used as replication condítion also.
Also have the application version updated from the template version when refreshed or replaced.
This would be nice but is limited to a fixed set of properties.
This document contains all the "Properties" stored as NotesItem.
As each organization has it's own reqirements, this can be adapted as neccessary.
This is not a user, but a database level property. I don't think there is a use case for versioning on organization level.


feasibility study for concrete block making industry in nigeria; 4.8 (2225 Ratings) ... hanson lake silica sand project mining property.
Feasibility Study Of Concrete Block., Buy Various High Quality Feasibility Study Of Concrete Block. Products from Global Feasibility Study Of Concrete Block.
a feasibility study of setting up a concrete block making... ... Profile Concrete Equipment is a leading supplier of brick and block making machines in Africa.
This page is about a feasibility study of setting up a concrete block making industry for sale price, ... Feasibility for Setting Up Concrete Block Making Industry.
medium scale concrete block production in nigeria; the feasibility report. ... medium scale concrete block production in nigeria; the feasibility report.


text:
Home Cryptocurrencies Indian Government is working to issue new Crypto Ban
Indian Government is working to issue new Crypto Ban
Ani khinikadze
Indian courts lifted the blanket ban on cryptocurrencies five months ago. However, an official stated that the government is considering a new law to ban cryptos again.
According to an Indian government official, the Reserve Bank of India and two ministries are actively working on a legal framework to ban cryptos on the subcontinent.
Furthermore, Indian news website Moneycontrol also wrote that authorities in India are making preparations to pass a law banning crypto trading. As the source claimed, consultations between the Ministry of Law and Justice, the Ministry of Electronics and Information Technology, and the Reserve Bank of India had begun about the framework of such a law.
The anonymous official added that, once Parliament resumes for the session, they will get the law ratified. Parliament will probably reconvene in late August or early September.
However, the government is considering banning crypto through legislative change, because it would be more binding. Earlier, the authorities used methods such as the blanket ban from the RBI for banks dealing with cryptocurrency companies. But this new method will define the illegality of the trade more clearly.
Cryptocurrency lows in India
In March, the Supreme Court of India voided a blanket ban on banks dealing with crypto businesses. The RBI had imposed the prohibition since July 2018. However, the repeal caused a boom in new exchanges across the country.
Despite that, government officials have been contemplating the idea of enacting a new law not allowing cryptos in India in place of the RBI ban.
Ashish Singhal, the CEO of Indian crypto exchange CoinSwitch, stated that the chances that the authorities would impose a new blanket ban on digital currencies were more probable in 2019 than this year. According to him, there has been a change in how crypto is perceived across India, hopefully for the better.
Many parts of India still face some restrictions on movement. This is due to the coronavirus pandemic, as a lockdown was ordered in March. Meanwhile, crypto exchanges in the country reported strong growth as some traders moved away from traditional assets.
TagsCryptocryptocurrencycryptocurrency news
Bitcoin gained 0.33% Monday. What about other cryptos?
Ethereum rallied by 0.69% Monday. What about Litecoin?
Which crypto trends can become more popular in 2021?
How will the crypto industry change in 2020?
Lending platform Vauld is growing into a full crypto bank
Litecoin fell by 0.09% Wednesday. What about Ethereum?
Ethereum declined by 0.43%. What about Ripple's XRP?
Bitcoin fell by 0.39% Friday. What about other currencies?
Litecoin lowered by 1.71% Thursday. What about Ripple's XRP?
Ethereum rallied by 0.47% Tuesday. What about Litecoin?
Sorrento Therapeutics gained 327% in 2020. Is it a Buy?
Bitcoins and an Anonymous Buyer with Wise Moves


The French are known for formality and politeness and at the table of the French, dining etiquette is absolutely a must. So how exactly do you go about having a meal with your French friends without offending? Keep reading to learn what to expect when dining out or in.
Given that the French are so in love with their food and its preparation, it only follows naturally that one must also have impeccable table manners to accompany the fine wine and dining. But be forewarned that what may look like beautiful table manners in America--is not in fact beautiful table manners in France.
For some reason, it is very rude to keep your hands in your lap while you are dining in France. It is equally rude to keep your elbows on the table and so the American diner must keep hands visible but elbows not. Also remember that the French almost never eat with their hands. This includes so called "finger foods."
Bread will always be served with your meal. If you are dining formally, bread will get its own plate. However, if you have no bread plate, the bread rests on the tablecloth and not on your plate. There is also a manner in which you should eat bread. While most Americans may take a bite out of the bread--the French consider taking a bite out of a whole slice of bread to be rather boorish. Instead, tear off the bread piece by piece. If you are using bread to soak up sauce, use it on the end of a fork.
The number one rule in French dining etiquette is to follow the host. If you do this and observe carefully, you will almost never err. This is particularly important when we're talking about beginning to eat, drink or anything else. In general, it is polite to wait until everyone is served and then the host will begin eating. Likewise, if there is an aperitif served, you should wait until the host raises her glass before you raise yours and take a drink.
Following the tips above will save you from embarrassment and making too many faux pas. While the rules of eating don't change drastically when you're eating out, there are a few special considerations to remember.
In America, the standard tip in a nice restaurant is between 15% and 20%. In France, tips are included. This is a French law so that the tips can be assessed for taxation purposes. You will see a service compris on your bill--which will be 15% of your food. However, one nice thing is that the price of food includes both the tip and the tax. So for example, if you order a piece of cake for $5 and a cup of coffee for $3, your bill is $8--service compris!
Who doesn't appreciate an extra tip? While you won't be considered rude for not tipping, it is an appreciative gesture to tip your waiter if he worked well. Something that many Americans don't realize is that the tip that is included in your bill does not necessarily go to the waiters. What's more, the owner of the restaurant can, by law, keep some or all of the tip. So anything additional you leave the waiter goes directly to him. So how much should you tip if you decide to tip extra? There is no hard and fast rule about percentages but if you consider about 5% of your check, this is a nice way to show gratitude to your waiter if he was especially diligent.
Eat your breakfast early in the morning when all the boulangeries are open.
Eat lunch some time between 12pm and 3pm.
Don't plan on much site seeing between 12pm and 3pm. This is standard lunch hour and things will be closed.
Plan on a late dinner. If you get too hungry before then, plan early to take a snack with you.
The best way to get along in France is to dine and eat the way the French do! Take later lunches and dinners, remember to follow the lead of your hostess and most of all observe the rules of politeness.


text:
Lynas to build commercial light rare earths separation facility in US
Australian rare earths miner Lynas has signed a deal with the US government to construct a commercial light rare earths separation plant in the country.
Lynas signs contract with US Government to build a rare earths separation plant. Credit: Peggy Greb, US Department of Agriculture.
The separation plant will be equipped to produce nearly 5,000 tonnes of rare earths products per year. This includes around 1,250 tonnes of neodymium and praseodymium (NdPr).
The facility will receive material directly from the cracking and leaching plant, which is currently underdeveloped phase by in Kalgoorlie, Western Australia.
The deal follows the signing of an agreement by Lynas with the US Department of Defense (DoD) in July 2020 to commence initial work on a heavy rare earth separation facility in Texas.
Sponsored by the Defense Production Act, the project will be executed in collaboration with the US Department of Defense.
Lynas plans to complete the light rare earths separation plant in accordance with the timetable of the DOD and as part of the company's 2025 plan.
Although detailed costings for the separation facility is due to be finalised, the company expects to contribute $30m million under the agreement and anticipates nearly $30m funding from the Department of Defense.
If the contract moves to the next phase, the Texas facility will have the capacity to accommodate processing facilities of heavy and light rare earths.
The facilities will cater to the defence industrial base as well as the growing commercial market, which includes electric vehicles and green technologies being developed in the US and in the rest of the world.
Lynas CEO and managing director Amanda Lacaze said: "This agreement is consistent with the US Government's commitment to rebuilding the domestic industrial base while working effectively with partner nations. The Texas plant will ensure the US has a secure domestic source of high quality separated Rare Earth materials.
"This secure supply will provide the essential foundation for the renewal of downstream speciality metal making and permanent magnet manufacturing in North America."
Extraction Technology in Mining: Ore Pre-Treatment
United States of America (USA) Mining Industry Fiscal Regime Analysis including Governing Bodies, Regulations, Licensing Fees, Taxes and Royalties, 2022 Update
Hydrogen in Mining - Thematic Research
Blockchain in Metals & Mining - Thematic Research
United States of America (USA) Copper Mining Market by Reserves and Production, Assets and Projects, Fiscal Regime including Taxes and Royalties, Key Players and Forecast, 2022-2026
Government of United States
Lynas Rare Earths Ltd
U.S. Department of Defense


WASHINGTON--(BUSINESS WIRE)--LeoSat Enterprises, which is launching a constellation of up to 108 low-earth-orbit communications satellites, has entered into a strategic agreement with the Globalsat Group, the leading Pan-American satellite services provider, to market the fastest, most secure and widest coverage HTS data network in the world.
The Globalsat Group is an award-winning industry leader delivering mission-critical, voice, data and M2M/IoT solutions. Through this agreement, LeoSat will provide the Globalsat Group with access to infrastructure for the Globalsat LEO Network, based on a high performance architecture pairing the speed of fiber with the ubiquity of satellite, and the Globalsat Group will provide LeoSat with access to the Americas market, leveraging its extensive presence and experience.
LeoSat's new system of low earth orbit communications satellites can deliver lower latency and stronger end-to-end security compared to traditional satellite and terrestrial solutions used today. This is achieved through a unique architecture utilizing inter-satellite laser links, creating an optical backbone in space with fiber-like symmetry at gigabit per second speeds. It also provides unprecedented security as the data is encrypted from end-to-end across the network, with no terrestrial touch points.
J. Alberto Palacios, CEO of Globalsat added: "By combining Globalsat Group's 17 years of industry experience and market access with LeoSat's innovative infrastructure, customers will use a game-changing service which redefines satellite connectivity in terms of capacity, latency, security, efficiency and coverage. This is possible through a system design combining proven and cutting edge technologies, leaps ahead of projects which look more like science fiction. We are thrilled to be part of one of the most important and promising upcoming satellite constellations in sight today".
Mr. Palacios will hold a seat in representation of the Globalsat Group on the LeoSat Customer Technical Advisory Committee (CTAC). The committee will advise on system configuration, product design and launch of LeoSat's upcoming satellite constellation.
LeoSat Enterprises was established in 2013 to leverage the latest developments in satellite communications technologies to develop and launch a new low-earth-orbit satellite constellation which will provide the first commercially available, business grade, extremely high-speed and secure data service worldwide.
With up to 108 low-earth-orbit communications satellites in the constellation LeoSat is the first company to have all of the High Throughput Satellites (HTS) in the constellation interconnected through laser links, creating an optical backbone in space which is about 1.5 times faster than terrestrial fiber backbones and without the need for any terrestrial touchpoints. This unique set of features enables LeoSat to provide instant infrastructure from anywhere to everywhere which is fast, secure and reliable.
Globalsat Group is the first Pan-American satellite service provider. The group is an industry leader providing Mobile Satellite Services (MSS) in Latin America since 1999 and has offices in the United States, Argentina, Bolivia, Brazil, Chile, Colombia, Peru and Mexico as well as distributors in the region's most important cities. Delivered solutions span all MSS service areas including land, sea and air, serving mobile satellite data and voice for thousands of customers in sectors such as Defense, Government, Utilities, Oil & Gas, Mining, Banking, Media, Agriculture, NGOs and Tourism.
The consortium received the "2016 Latin America Satellite Communications Company of the Year" award from the highly recognized international consulting firm Frost & Sullivan. Globalsat Group was also named "Company to Watch" in the category Emergency Response Mobility Satcom Innovation by the Mobile Satellite Users Association (MSUA).


text:
GTAWU warns of Heightened Industrial Action against NAWASA
As the Board of Directors and Management of the National Water and Sewage Authority (NAWASA) continue to hold out and defy the Grenada Technical and Allied Workers Union's (GTAWU) calls to regularized the scores of workers who have been operating on contract for years, union has given its strongest indication to-date that Grenada could be facing a national strike.
Addressing members of the media during a press briefing at the union's headquarters in St George's last Friday in the presence of a number of contracted NAWASA workers, TAWU's president General Andre Lewis noted that after meeting union members and shop stewards from various private and public entities on the island it was unanimously agreed that additional pressures should be brought on NAWASA to achieve the desired result.
Lewis indicated that a number of entities among them Grenlec, and Air Traffic Control, Met. Office and the Maintenance Department at the Maurice Bishop International Airport, Grenada Port Authority, National Bus Terminus among others have agreed to give solidarity support to the struggle now faced by the NAWASA workers.
The President General noted that based on these pledges and the refusal of NAWASA to resolve the matter, the nation could look forward to increased industrial action as of this week.
The ongoing TAWU/NAWASA impasse started early December with the call for all contract workers to be made permanent, effective from the date of their employment.
That offer was rejected by the NAWASA negotiating team, and therefore on the advice of the union, workers withdrew their services just before the Christmas and remain on the picket line to the present date.
Lewis called on the nation to be on guard, for the possible impact this situation may have on their normal daily functions. He, however, noted that the ball is in the court of the government to do what is necessary to prevent an escalation of this matter. TAWU, he said is open for discussion, however, they are not prepared to change their course of action.
As it stands Lewis said, it is just a matter of time before the green light is given for the increased action, and although it is not something that TAWU wants to do, the present situation leaves them with no choice and therefore would do what is best for the workers.
Lewis calls for public understanding in the situation since this is an issue that touches and concerns the bread and butter of their workers and therefore the time has come to put an end to an issue that has gone on for way too long.
The President General said having been given the commitment; TAWU would determine the course of action and time.
Although the present issue touches and concerns NAWASA Lewis said a number of other companies are in similar situations and TAWU would soon be moving to address concerns- among them, the exploitation of workers in other workplaces as soon as the NAWASA situation is put to rest.
Among the companies listed were Caribbean Agro Industries, Grenada Broadcasting Network, and Calabash Hotel, among others.
NNP Activist accused of soliciting support for Government one-off payment
Also coming out of last Friday's press briefing is information that hinges on political interference in the battle of the Government one-off payment to public workers
Lewis hinted to members of the media, that information has reached the union that a political activist of the ruling New National Party has been going around the government ministries asking public workers to sign a petition agreeing to accept the government one-off payment offer to public workers.
While some workers including the Police we were told, accepted the offer, workers attached to the GTAWU, the Grenada Union of Teachers and the Public Workers Union, PWU, remain adamant they would not accept the $750 one-off payment offered by the government.
In light of the present situation, Lewis noted that this development is wrong and calls on the activist to cease such practice.
As it related to the organizations that went ahead and accepted Government's offer, Lewis said this is their right and he respects that but noted that TAWU would not accept that offer.
2018 Soccer Almanac: Key dates to mark in the year ahead - SoundersFC.com
Wed Jan 3 , 2018
2018 Soccer Almanac: Key dates to mark in the year ahead
SoundersFC.com
January 2-11: U.S. Soccer Men's YNT Summit Camp, Lakewood Ranch, Fla. For the first time ever, US Soccer has gathered its five oldest youth national teams (U-16s, U-17s, U-18s, U-19s and U-20s) in one place to begin preparations for the Under-17 and ...
Spice Island Beach Resort's Sir Royston Hopkin Bestowed Prestigious Trail Blazer's Award
admin 1 year ago
More than 130,000 Students Across the Caribbean to Benefit from Virtual Learning Platform
34 year-old St. John's resident slapped with drug trafficking charge
Drug Bust in Happy Hill- one man on EC$200,000.00 bail
Third Reshuffle Includes A New Face
RGPF Honors Its Retirees
Clouden calls for DECRIMINALIZATION OF MARIJUANA
Visitor Attacked at Her Majesty's Prison
Veterinary Student Acknowledged for Excellence in Small Animal Neurology
Rearing To Go In Weekend Competitions
Weekend Fire Leaves Two Cherry Hill Families Homeless
DWELLING HOUSE RAIDED Occupants Caught Processing Crack Cocaine


text:
'Star Wars Rebels: Complete Season Two' Blu-ray Review: Rise of the Rebellion
September 7, 2016Ben MK
After contending with the relentless Agent Kallus (David Oyelowo) and vanquishing the merciless Grand Inquisitor (Jason Isaacs) in Star Wars Rebels season one, the crew of the Ghost find themselves up against a much more formidable adversary in season two — namely, the Sith Lord Darth Vader (James Earl Jones) himself.
Now, fighting side-by-side with the Rebellion's Phoenix Squadron, Hera Syndulla (Vanessa Marshall), Sabine Wren (Tiya Sircar), Kanan Jarrus (Freddie Prinze Jr.), Zeb Orrelios (Steve Blum), Ezra Bridger (Taylor Gray) and Chopper the Astromech are teaming up with The Clone Wars' Ahsoka Tano (Ashley Eckstein) and her old ally, Captain Rex (Dee Bradley Baker). Meanwhile, Vader dispatches his vast legions of Imperial forces, as well as more Inquisitors (Philip Anthony-Rodriguez and Sarah Michelle Gellar), to hunt them down, in the hopes that capturing Anakin Skywalker's former Padawan will lead them to the other missing Jedi, such as Obi-Wan Kenobi.
Along the way, the Ghost crew engage in a few side-missions, like getting entangled in a quarrel among space pirates in "Brothers of the Broken Horn," rescuing younglings from the Inquisitors in "The Future of the Force," and recruiting an elite Mandalorian warrior to join the Rebellion in "The Protector of Concord Dawn." What's more, in addition to the iconic Darth Vader, season two also includes appearances from original trilogy characters like Lando Calrissian, Princess Leia Organa and Master Yoda. Plus, there are more fun, little Easter eggs for Star Wars fans to discover, as in "Wings of the Master," which reveals the never-before-told origins of the Rebel fleet's B-Wing.
All in all, season two of Star Wars Rebels proves to be a rousing continuation of the series, delivering more of what Star Wars fans love, as well as drawing integral connections between the show and The Clone Wars, the original trilogy, and even The Force Awakens. As for this season's twenty-two episodes, they break down as follows:
The Siege of Lothal (Parts I and II) - The Inquisitor is dead. The Ghost crew has connected with other rebel cells. And a new ally named Ahsoka Tano has emerged. Despite these successes and developments, the fight against the Empire takes a deadly turn, as the evil Sith Lord Darth Vader comes to Lothal.
The Lost Commanders - Ahsoka Tano sends the Ghost crew to Seelos in search of an old friend — one whose leadership and strategy skills could help the fledgling rebellion. But will this legendary commander be willing to join the fight?
Relics of the Old Republic - While Kanan continues to struggle with trust issues, the other rebels begin to form friendships with the old clones. And when Agent Kallus arrives, all must join together to battle the Imperials.
Always Two There Are - Thanks to Rex's intel, Ezra, Sabine, Zeb, and Chopper head out to an abandoned Republic medical station with the hopes of finding much needed supplies. When they encounter new enemies, however, the stakes become much higher.
Brothers of the Broken Horn - When Ezra answers a distress signal from the Broken Horn, the young Jedi finds someone unexpected waiting: the legendary pirate Hondo Ohnaka. But is he friend or foe?
Wings of the Master - With the rebels in desperate need of a ship with heavy weaponry, Hera seeks out a master engineer who has built a powerful new starfighter prototype.
Blood Sisters - While on mission to rendezvous with a courier holding secret information, Sabine encounters someone from her past: a bounty hunter named Ketsu. But is she friend or foe?
Stealth Strike - When the Empire uses a powerful new weapon to capture Ezra and Commander Sato, Rex and Kanan must put their differences aside to save their friends.
The Future of the Force - After the Empire's Inquisitors begin targeting select babies for abduction, Ahsoka Tano and the Ghost crew investigate. What they find is unsettling, and it all leads to a deadly confrontation with the children's fates hanging in the balance.
Legacy - After seeing his parents in a strange vision, Ezra believes they may still be alive. He heads back to Lothal for answers, while the Empire comes to Garel hoping to crush the rebellion.
A Princess on Lothal - While Ezra grapples with the news about his parents, the rebels make plans with Senator Bail Organa to secure three much-needed cruisers. Leading the mission is an agent hand-picked by the Senator: his daughter, Leia.
The Protector of Concord Dawn - Looking to secure a new hyperspace route to Lothal, the rebels head to the Mandalorian-controlled Concord Dawn to negotiate safe passage for their fleet. The warrior Protectors of the system prove to be less than welcoming, however, and it's up to Kanan and Sabine to turn this group into friends... or enemies.
Legends of the Lasat - Thanks to intel from the space pirate Hondo, the Ghost crew rescue two Lasat from Imperial clutches. These survivors believe Zeb is the key to a prophecy that will lead to a new home for their kind — but Zeb, conflicted and ashamed of his failure to save Lasan, has little faith.
The Call - Low on fuel and power in deep space, the Ghost crew encounters massive, mysterious creatures whose lives are threatened by a mining operation.
Homecoming - The Ghost crew joins forces with Cham Syndulla, father of Hera and Clone Wars legend. But will his thirst for revenge — and fractured relationship with his daughter — cost the rebels a victory?
The Honorable Ones - Zeb and Agent Kallus find themselves stranded on an icy moon of Geonosis after a failed Imperial ambush of the rebels. Bitter enemies, they must put aside their differences and work together in order to survive.
Shroud of Darkness - Kanan, Ezra, and Ahsoka return to the Jedi Temple on Lothal, seeking to learn how the Inquisitors continually track them. Each has a different experience, and nothing will ever be the same.
The Forgotten Droid - When Chopper steals a replacement for his original leg, he separates from the Ghost crew and finds himself stranded on an Imperial ship. The grumpy astromech meets an inventory droid in service of the Empire, but will this new acquaintance become friend or foe?
The Mystery of Chopper Base - The rebels finally locate a potential site for a secret base, but find their new home is not as isolated as originally believed...
Twilight of the Apprentice (Parts I and II) - Ezra, Kanan, and Ahsoka arrive at Malachor, a seemingly dead world and home to an ancient Sith Temple, but they are not alone. Paths cross, destinies change, and fates are fulfilled.
AUDIO & VISUALS:
As with season one of Star Wars Rebels, season two boasts a flawless 1080p image presentation. The show's CG animation is crystal-clear and razor-sharp; colors are robust, from the varying shades of grey and neutral tones of the Empire, to the more vibrant hues of the Rebellion; and black levels and contrast are top-notch, from Vader's sleek black armor to the stark black-and-white color scheme of the Stormtroopers. As for the audio, however, season two is outfitted with yet another Dolby Digital 5.1 presentation. And while dialogue, the familiar Star Wars musical themes, and sound effects like blaster fire, spaceship fly-bys and the low-frequency humming of lightsabers sound just fine with lossy audio, the lack of a lossless option is simply a missed opportunity.
Disney's three-disc Blu-ray release includes the following Blu-ray extras:
Rebels Recon (2:10:07) - StarWars.com's Andi Gutierrez hosts these brief, behind-the-scenes looks at each of season two's 22 episodes, which feature interviews and Q&A tidbits with LucasFilm Story Group's Pablo Hidalgo, Executive Producer Dave Filoni, and the cast and crew behind the show.
Connecting the Galaxy: Rebels Season 2 (3:30) - A look at the "Easter eggs, hidden stories and epic connections" that link the show to the rest of the Star Wars universe, such as the ties to The Force Awakens and an homage to artist Ralph McQuarrie.
From Apprentice to Adversary: Vader vs. Ahsoka (6:08) - Executive Producer Dave Filoni talks about the epic confrontation between Ahsoka Tano and Darth Vader that caps off season two, as well as the chain of events from The Clone Wars animated series that led to it.
Star Wars Rebels: Complete Season Two is available from Walt Disney Studios Home Entertainment as of August 30th, 2016. Episode synopses above provided courtesy of Starwars.com. The Blu-ray features English Dolby Digital Audio 5.1, French Dolby Digital 5.1, Spanish Dolby Digital 2.0 and German Dolby Digital 5.1 tracks. The film is presented with English, English SDH, French and Spanish subtitles. The total runtime is 8 Hrs. 5 Mins.


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Charles Lindbergh Stallings was born on December 14, 1927 to Ida and John W. Stallings. John passed away when Lindbergh was about one year old and his mother's family bonded together to raise him, just as they did through the years for many other family members. Taking a village to raise a child was commonplace during that time.
Lindbergh's first job was at the age of thirteen years old when he stamped peaches in Yatesville for seven cents per hour. He then became an entrepreneur and started a shoe shine business where he charged customers ten cents per pair of shoes. Although the school in Yatesville had eleven grades, Lindbergh quit after the tenth year to work full time. He worked at Martha Mills for forty cents per hour inspecting yarn. Lindbergh moved to work at the Bleachery in Thomaston until World War II was over. Shortly thereafter, he was drafted due to the Korean War and served 23 months in the Army in Korea, in L Company - 45th Infantry. He made life-long friends in service who got together every year; on even years, they would meet in Calhoun, Georgia and in odd years they would meet somewhere in the west. He continued this tradition of sharing time with his brothers in arms until 2012.
For many years of his life, Lindbergh lived an exciting life playing cards with his buddies and renting out pool tables and other games. He married Verna Conley Howard and had an instant family with his two step children. Lindbergh also was a father of many in Yatesville in that he adopted and loved all of the children in town as they adopted and loved him. He would have cookouts and have all of the children playing on pool tables and video games in his basement. He hosted many birthday parties, gatherings for the Georgia Baptist Children's home, the youth of Yatesville Baptist Church, and other spontaneous events. He took the "village raising the child" concept from his childhood to heart and took it upon himself to continue that tradition.
Lindbergh joined Yatesville Baptist Church and believed that God loves us all and forgives us of our sins. He loved to laugh and play cards or checkers with anyone who had time to sit a while. The stories of his life would certainly fill a book. He helped people behind the scenes, not ever wanting credit for it. He will be missed by so many. Just ask anyone who knew him.
Charles Lindbergh Stallings went to meet his heavenly Father on March 17, 2015. He is preceded in death by his wife. He is survived by his two step children, four grandchildren, several great-grandchildren, a great-great grandchild, several nieces and nephews, several great nieces and great nephews and many dear friends.
Funeral services for Mr. Stallings were held on Friday, March 20th, 2015 at 2 pm at the Yatesville Baptist Church. Rev. John Wesley Long and Rev. Steve Maguire officiated and burial followed in the New Hope Primitive Baptist Church Cemetery.