Questions tagged [anti-de-sitter-spacetime]
Anti-de-Sitter (AdS) spacetime is a spacetime with a constant negative Ricci Scalar.
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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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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 ...
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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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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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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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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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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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Why don't we have Poincare coordinate for de Sitter space unlike Anti de Sitter space?
My understanding is that you get de Sitter space from Anti de Sitter space, if you change $l^2$ to $-l^2$. However, why can't I find Poincare coordinate for de Sitter space, if Anti de Sitter space ...
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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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ADM Formalism in Anti-de Sitter
While there different ways of defining energy in anti-de Sitter spacetimes in GR (cf. for example arXiv:2209.09031), I never see anyone discussing the ADM formalism in AdS. Does anybody know why that ...
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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
$$S_{\text{EH}} = ...
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Are different "topological" AdS spacetimes isometric?
In this paper https://arxiv.org/abs/hep-th/9808032 the author says that black holes in AdS spacetimes can have horizons with different topologies. In particular, when the black hole mass $M$ vanishes, ...
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Momentum Operator in Anti de Sitter spacetime
Im studying the dirac equation in two dimensional anti de sitter space with metric
\begin{align*}
g_{\mu\nu}= -\frac{L^2}{\cos^2(\theta)}\left( \begin{array}{rr}
1 & 0 \\
0 & -1
\end{array}\...
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Is the non-simply connected version of AdS space a maximally symmetric spacetime?
A common construction of anti-de Sitter space is the following:
Start with the flat five-dimensional manifold with metric $ds_5^2 = -du^2 - dv^2 + dx^2 + dy^2 + dz^2$.
Consider the hyperboloid ...
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Boundary condition on wave in Schwarzschild-Anti-deSitter spacetime at event horizon
I am trying to model the behaviour of a spherical symmetric wave near a black hole in asymptotically Anti-de-Sitter spacetime. The metric for such a spacetime in Eddington-Finkelstein-coordinates is
$$...
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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
$$
how can we show that this metric is asymptotically Euclidean AdS? Specicifally, when $\tau\rightarrow\pm\infty$ is it ...
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AdS-CFT correspondance from 1D to 4D
From what I understand the AdS-CFT correspondence states that the bulk dynamics of a $n$-dimensional gravitational theory are encoded in the degrees of freedom of its dual CFT in the $(n-1)$ ...
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AdS$_4$ and $\mathbb{H}^4$: What is the difference between them?
This figure (source) shows the embedding of 4D hyperbolic space $\mathbb{H}^4$ and 4D de Sitter space dS$_4$ in 5D Minkowski space $\mathbb{M}^5$. $\mathbb{H}^4$ is a hyperboloid of two sheets and dS$...
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Scalar field theory boundary term in AdS
In AdS we can have the following action
$$
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
$$ \dfrac{1}{2\kappa^2}\int d^4x \; e \left[R(\omega) - \bar{\psi}_\mu \gamma^{\...
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How to obtain the metric(s) from an action?
So I am confused about dimensional reduction. Because most litterature that I have found so far jump over the steps where they obtain the corresponding metric(s) from some action.
In particular, I ...
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AdS$_D$ relation killing vector and boost
I am following "Supergravity" from Freedman and Van Proeyen and I am working on problem 22.8 therein.
They embedded AdS$_D$ in $\mathbb{R}^{D+1}$ as $$f(Y)=-(Y^0)^2+\sum_{i=1}^{D-1} (Y^i)^2 -...
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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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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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How to derive the AdS spacetime metric
So I have been working on AdS/CFT for a while now and realized that I have never actually seen the derivation for the metric. In every literature, introductory or advanced, they just give you the AdS ...
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Two-twistors formulation vs twistors formulation
I have seen in some research work that the classic formulation using twistors (introduced by Penrose) is replaced with a formulation that considers two-twistors.
For example the linking article says ...
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Is there any place in an AdS Universe with positive spacial curvature?
An AdS space has constant negative curvature, gravitational objects introduce more negative curvature. Therefor it seems like it is possible that everywhere in the Universe has negaative curvature (...
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Directly solving equation of motion in embedding space coordinates
If you're given a manifold as an embedding, how does one solve an equation directly in the embedding space coordinates?
Specifically, I am trying to solve the equation
$(\nabla_{\mu}\nabla_{\nu}-g_{\...
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Stress-energy tensor of a scalar theory in AdS
In this review of the AdS/CFT correspondence, going through section 2.2.2 I am not quite sure where the stress-energy tensor
$$
T_{\mu\nu}=2\partial_\mu\phi\partial_\nu\phi-g_{\mu\nu}\left((\partial\...
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Ricci scalar of AdS in $D$ spacetime dimensions from structure equations
Starting from the AdS metric in $D$ spacetime dimensions in Poincare coordinates $ds^2 = \frac{R^2}{(x^3)^2}\eta_{\mu\nu}dx^\mu dx^\nu$ (R here is the AdS radius), I would like to compute the ...
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Anti de Sitter & de Sitter Spacetime [duplicate]
Can anyone please explain what are the Anti de Sitter and de Sitter spacetime and what is special about them? I am learning general relativity and I stumbled upon them a few times, even on the subject ...
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Can I just add a cosmological constant to an on-shell supergravity action?
Suppose one has some supergravity Lagrangian $\mathcal{L}_\text{sugra}$ in flat (Minkowski) space. Moreover, assume that this Lagrangian is on-shell, in the sense that the auxiliary fields have been ...
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Anti de Sitter metric with signature +---
Most of the textbooks write EFE
$$ R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R=-\Lambda g_{\mu\nu} $$
With metric signature $-+++$. However, I am using the other signature $+---$, but when I solve for Anti de ...
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Derivation of $zz$-component of Einsteins Equations in AdS
I am trying to understand how we get the Einsteins equations in here section 4.1 equation 4.2 where we use the metric
$$
ds^2 = a^2(z)(dz^2+dx^\mu dx_\mu)
$$
to derive the $zz$-component of Einstein's ...
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Difference between asymptotically AdS and asymptotically locally AdS spacetime
In the literature, there is often a distinction made between spacetimes that are asymptotically or asymptotically locally some other spacetime. For example, in holography, referring to some spaces ...
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AdS/CFT spacetime visualization
I was inspired by comments under this answer to ask this question.
In the context of AdS/CFT, one often finds an embedding diagram of the $10d$ spacetime that I don't find particularly enlightening, ...
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Flat space limit of the $AdS$ metric: Very basic question
Suppose I am given the following global coordinates in empty $AdS_n$:
$$ds^2 = \alpha^2\left(-\cosh^2\rho \, d\tau^2 + \, d\rho^2 + \sinh^2\rho \, d\Omega_{n-2}^2\right)$$
where the length scale $\...
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Isometries or Isometry direction of $AdS_5 \times S^5$
This is a consequent question with my previous question https://physics.stackexchange.com/q /610501/
I want to know the isometries (or isometry direction) of $AdS_5 \times S^5$. Usually, when we ...
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Metric form of $AdS_5 \times S^5$
I want to know the metric form of $AdS_5 \times S^5$.
I know there are two forms (maybe more?) Poincare patch and global patch.
And what is the difference between these two patches?
Can you state the ...
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