Questions tagged [anti-de-sitter-spacetime]
Anti-de-Sitter (AdS) spacetime is a spacetime with a constant negative Ricci Scalar.
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Rewriting the Euclidean on-shell action of Schwarzschild-AdS
The Schwarzschild-AdS solution is given by
\begin{align}
\label{eq: Schwarzschild-AdS metric}
ds^2=-f(r)dt^2+\frac{dr^2}{f(r)}+r^2d\Omega^2\,,
\end{align}
where
\begin{align}
f(r)=1-\frac{2MG}{r}-\...
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Why is AdS-boundary considered timelike?
I was wondering why the conformal boundary of (compactified) AdS is said to be timelike. Consider the conformal compactification of AdS spacetime with metric
$$g = (- dt^2 + dx^2 + \sin^2 x \ d\Omega^...
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Can we have negative Ricci scalar?
Recently I faced a negative Ricci scalar in some calculations and looking for a physical interpretation for it. Is there any physical Energy-Momentum tensor that could produce a negatively signed ...
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Why is hyperbolic space needed in AdS / CFT?
Is there a reason why a hyperbolic bulk is needed in AdS/CFT (other than the name suggests it must be an AdS)?
In other words would a flat or positively curved bulk, work with the CFT correspondence? ...
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When dealing with a space like $AdS_5$, why can we take the universal cover?
In the context of the AdS/CFT correspondance, when considering $AdS_5$ we can pick the coordinates
$$x_0=R\:cosh(\rho)\: cos(\tau)
\\ x_5=R\:cosh(\rho)\:sin(\tau)
\\ x_i=R\:sinh(\rho)\:\hat{x}_i,\;\;\;...
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Are de Sitter, Anti-de Sitter and Minkowski spaces spatially infinite?
I am not someone who has studied general relativity, however have recently developed an interest in it. From what I have seen online, de Sitter, Minkowski and Anti-de Sitter spaces are often compared ...
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Robin conditions from action principle
Consider the Lagrangian density
$$L(\tilde{\phi}, \nabla \tilde{\phi}, \tilde{g}) = \tilde{g}^{\mu \nu} \nabla_{\mu} \tilde{\phi} \nabla_{\nu} \tilde{\phi} + \xi \tilde{R} \tilde{\phi}^2$$
with $\...
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Conformal compactification of AdS spacetime
In this paper https://homes.psd.uchicago.edu/~ejmartin/course/JournalClub/Basic_AdS-CFT_JournalClub.pdf, page 2, the authors state "The boundary of the conformal compactified $AdS_{d+1}$ is ...
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How do I prove that inversion and translation are an isometry in AdS?
I am using the AdS metric in Poincare coordinates, meaning $$ds^2 = \frac{R^2}{z^2}(dz^2 + d\vec{x}^2)$$
I want to prove why inversion $x^{\mu} = \dfrac{x'^{\mu}}{x'^2}$ and translation $x'^{\mu} =x^{\...
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Killing Vectors AdS$_3$
I have been trying to understand the Killing vectors of AdS$_3$,i.e. Anti de Sitter in three dimension:
$$
ds^2 = dX^2 + dY^2 -dU^2 -dV^2
$$
In this case the generators are given by $J_{ab}=x_a \...
4
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How does the bulk-to-boundary propagator transform under diffeomorphisms?
In AdS/CFT, the bulk-to-bulk propagator can be obtained as the limit of the bulk-to-bulk
propagator with one point approaching the boundary. For example in the scalar case
\begin{equation}
K_{\Delta}(...
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Is it correct to claim that Hawking-Page phase transition is related to the breaking point at the Page-time?
In the evaporation process of a Black Hole in an AdS space we have a Hawking-Page phase transition. We know that such a phase transition can be exhibited by a singular behavior. At the other hand, ...
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Global Hyperbolicity and Timelike Boundary
I am trying to understand and show that asymptotically Anti-de Sitter spacetimes are not globally hyperbolic.
Now, I have found papers that talk about global hyperbolic spacetimes with timelike ...
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Negative $\Lambda$ FLRW spacetimes as infinite black holes?
Consider the Friedmann equation:
$$H^2+\frac{k}{a(t)^2} = \frac{\Lambda}{3}+\frac{8 \pi}{3}\rho$$
and set the parameters for dust in either flat euclidean or open hyperbolic spatial slices with a ...
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Gravity dual of the string world-sheet CFT?
The AdS/CFT correspondence conjectures a duality between a $(D+1)$ dimensional gravity theory in asymptotic AdS spacetime with a $D$ dimensional conformal field theory. Is there any sense in asking ...
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AdS compactification of Minkowski space
I am trying to understand the paper "Anti De Sitter Space And Holography" by E. Witten (cf. https://arxiv.org/abs/hep-th/9802150).
One of the first point it makes is that "Minkowski ...
3
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0
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Asymptotic AdS and coordinate change
I'm confused that boundary condition in 2d AdS spacetime. In two dimensions, we can write the metric in conformal gauge,
\begin{align}
ds^2=e^{2\omega(u,v)} dudv.
\end{align}
Suppose we impose the ...
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Conformal mapping of Euclidean Schwarzschild AdS black hole
I have been trying to understand this for some time. given the Euclidean S-AdS black hole metric,
$$ ds^2 = f(r)d\tau^2 + \frac{1}{f(r)} dr^2 + r^2d\Omega^{2}_{D-2} $$
From what I understand this has ...
1
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1
answer
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Need for boundary conditions in AdS space?
I am referencing to a passage on wikipedia's page about AdS space:
Because the conformal infinity of AdS is timelike, specifying the initial data on a spacelike hypersurface would not determine the ...
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votes
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Penrose Diagram for AdS black hole
I am trying to construct the Penrose diagram of a black hole in AdS space. Now, I thought I was on a good track, my diagram looked like this:
The grey lines are the surfaces of constant $t$ and ...
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Does AdS/CFT correspondence apply to entire AdS space or those covered by Poincare patch?
I am getting confused as I study the AdS/CFT correspondence, so I ask this question. CFT is given on the conformal boundary of AdS, which can be derived from Poincare coordinate patch to AdS. Would ...
2
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1
answer
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Carter Constant with a Cosmological Constant
The Carter constant for the Kerr Newman metric
$$ \rm C = p_{\theta}^{2} + \cos^{2}\theta \ \Bigg[ a^2 \ (m^2 - E^2) + \left(\frac{L_z}{\sin\theta} \right)^{2} \Bigg] $$
with (in $[+---]$ signature)
$$...
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Properties of anti-deSitter space
I have some questions about anti-deSitter space, (note: I am not a physicist)
When describing deSitter space it is almost always mentioned that it has a positive cosmological constant and is therefore ...
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1
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Is AdS repulsive?
Is Anti de Sitter spacetime repulsive because of its negative scalar curvature? Will a fluid flowing radially inward experience an opposition that has a radially outward component? And how can one ...
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0
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Curvature length and Newton's constant in AdS
What is the dimensions of Newtons gravitational constant in arbitrary dimensions in terms of teh curvature radius?
I am looking at entanglement entropy which goes as $S \sim \frac{ l_4^2}{G_4}$. This ...
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2
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Getting confused with different metrics for AdS black hole
I'm getting confused with the convention for the metric that describes a (planar) AdS black hole in $1+d$ dimensions ($1$ timelike, $d$ spacelike).
The most common definition seems to be the one as in ...
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AdS, nearly AdS, and asymptotically AdS
Recently, I took a seminar about JT gravity, and the speaker said about exact Ads, nearly Ads, and asymptotically Ads.
I want to know the difference(i.e., the form of metric? or the conditions on ...
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Naive questions on AdS/CFT dictionary and alternatives?
I'm starting to become curious about AdS/CFT since hearing that condensed matter theorists use it as a 'dictionary' to find gravity duals of things from condensed matter physics. How exactly does this ...
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0
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Understanding classically equivalent actions of the same physical theory - what went wrong as they produce different E.O.M? [duplicate]
I am working on a specific example where the metric I am using is the $AdS_4$ metric whose ricci scalar $R=-12/l^2$ for some characteristic scale $l$: $$ds^2=-\cosh^2\left(\frac{\rho}{l}\right)dt^2+d\...
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How to move from AdS to dS space?
I studied different black holes in different spacetime and I also checked their differences, for example, the difference that exists in dS and AdS spaces. The question that has been created for me is ...
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In AdS/CFT, do we have Weyl-invariance or only conformal invariance?
The asymptotic symmetry group of $AdS_{d+1}$ is $SO(d,2)$, which just so happens to be the conformal group of $d$-dimensional Minkowski spacetime. Therefore the boundary dual, if it exists, has ...
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What is the symmetry group of asymptotically AdS spacetime?
The isometry group of global $AdS_{d+1}$ is well-known to be $SO(d,2)$. I have a suspicion that when the spacetime is asymptotically AdS, with dynamical gravity in the bulk, the symmetry group gets ...
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Penrose diagram of Schwarzschild-AdS space
I want to construct the conformal Penrose diagram for the Schwarzschild Anti-deSitter spacetime (SAdS). However, I am having trouble eliminating the coordinate singularity at the event horizon. My ...
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Cosmological constant of $\text{AdS}_5 \times S^5$
I have a quick question about the Einstein-Hilbert action $S_{\text{EH}}$ action with cosmological constant regarding $\text{AdS}_5 \times S^5$ spacetime. $S_{\text{EH}}$ is given by
$$S_{\text{EH}} = ...
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Are different "topological" AdS spacetimes isometric?
In this paper https://arxiv.org/abs/hep-th/9808032 the author says that black holes in AdS spacetimes can have horizons with different topologies. In particular, when the black hole mass $M$ vanishes, ...
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Momentum Operator in Anti de Sitter spacetime
Im studying the dirac equation in two dimensional anti de sitter space with metric
\begin{align*}
g_{\mu\nu}= -\frac{L^2}{\cos^2(\theta)}\left( \begin{array}{rr}
1 & 0 \\
0 & -1
\end{array}\...
- 507
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1
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Is the non-simply connected version of AdS space a maximally symmetric spacetime?
A common construction of anti-de Sitter space is the following:
Start with the flat five-dimensional manifold with metric $ds_5^2 = -du^2 - dv^2 + dx^2 + dy^2 + dz^2$.
Consider the hyperboloid ...
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Stress- energy tensor in AdS
I´m trying to reproduce some of the equations from the paper
-- A Stress Tensor For Anti-de Sitter Gravity, by Balasubramanian and Kraus,
https://arxiv.org/abs/hep-th/9902121 -- and I keep getting one ...
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Infinite value of fields
I was reading this article Scalar propagators on AdS Space by Harold Erbin, where the author attempts to find the classical solution of the massive scalar field in AdS space. To discard one of the ...
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BTZ black hole and thermal $AdS_3$
Why is Euclidean $BTZ$ black hole at temperature $T$, equivalent to thermal $AdS_3$ at temperature $1/T$?
I'm not really familiar with those objects, but I have used the modular transformation
$$\tau_{...
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Euclidean BTZ black hole dual to thermal CFT state
I'm studying $\textbf{Holographic Derivation of Entanglement Entropy from AdS/CFT}$ by Shinsei Ryu and Tadashi Takayanagi.
I'm trying to compute the entanglement entropy in $CFT_2/AdS_3$ at finite ...
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How can can we show that a metric is asymptotically AdS?
Given any metric, for example
$$
ds^2=d\tau^2+L^2\cosh(H\tau)d\vec{x}^2
$$
how can we show that this metric is asymptotically Euclidean AdS? Specicifally, when $\tau\rightarrow\pm\infty$ is it ...
- 2,035
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AdS-CFT correspondance from 1D to 4D
From what I understand the AdS-CFT correspondence states that the bulk dynamics of a $n$-dimensional gravitational theory are encoded in the degrees of freedom of its dual CFT in the $(n-1)$ ...
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AdS$_4$ and $\mathbb{H}^4$: What is the difference between them?
This figure (source) shows the embedding of 4D hyperbolic space $\mathbb{H}^4$ and 4D de Sitter space dS$_4$ in 5D Minkowski space $\mathbb{M}^5$. $\mathbb{H}^4$ is a hyperboloid of two sheets and dS$...
- 713
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0
answers
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Scalar field theory boundary term in AdS
In AdS we can have the following action
$$
S=\frac{1}{2}\int_\mathcal{M}{d^{d+1}x\sqrt{-g}\phi(g^{\mu\nu}\partial_\mu\partial_\nu+m^2)\phi}-\frac{1}{2}\int_{\mathcal{M}}d^{d+1}x\sqrt{-g}\partial_\mu(g^...
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Anti-de Sitter superalgebra from preserved symmetry
Following Freedman & Van Proeyen's "Supergravity", the $\mathcal{N}=1,\, D=4$ AdS supergravity action is
$$ \dfrac{1}{2\kappa^2}\int d^4x \; e \left[R(\omega) - \bar{\psi}_\mu \gamma^{\...
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How to obtain the metric(s) from an action?
So I am confused about dimensional reduction. Because most litterature that I have found so far jump over the steps where they obtain the corresponding metric(s) from some action.
In particular, I ...
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votes
1
answer
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AdS$_D$ relation killing vector and boost
I am following "Supergravity" from Freedman and Van Proeyen and I am working on problem 22.8 therein.
They embedded AdS$_D$ in $\mathbb{R}^{D+1}$ as $$f(Y)=-(Y^0)^2+\sum_{i=1}^{D-1} (Y^i)^2 -...
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answer
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How is AdS/Schwarzschild asymptotically AdS?
A simple GR question. Consider planar Schwarzschild-AdS solution $$ds^2=\frac{R^2}{z^2}\left(-fdt^2+dx^2+\frac{dz^2}{f}\right)$$ where $f=1-(z/z_0)^d$ for constant $z_0$. I've heard this referred to ...
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votes
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Why is AdS spacetime like a "saddle"?
When the shape of the universe is discussed, the three cases are flat, closed and open. Where AdS spacetime with a negative cosmological constant describes the open spacetime, as in the middle in the ...
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