Questions tagged [anti-de-sitter-spacetime]

Anti-de-Sitter (AdS) spacetime is a spacetime with a constant negative Ricci Scalar.

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Does there exist charged BTZ black hole analogue in 1+3D with a negative cosmological constant?

BTZ black holes are defined for the case of 1+2D gravity theory because of closed form computation. I’m wondering if there exist a $1+3D$ analogue black hole? Edit: What I'm actually looking for is ...
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A question about the recent study that supports the Holographic Principle

First off, I agree with Susskind. There's no way to get around the Holographic universe. Maybe there will be one day, but each year it gets stronger and stronger. There's simply a limit to the ...
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Does one observe light reach infinity in finite time in AdS spacetime?

I have a question about the following passage from this article: Moschidis imagined standing in the middle of AdS space-time, which would be like standing inside a giant ball whose edge or boundary ...
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What's the right way to include the characteristic length in the metric of a maximally symmetric space in General Relativity?

Given a maximally symmetric space with characteristic length $L$, I have seen different conventions when writting the factor explicitly in the metric, and I wonder if any interpretation is more ...
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The range of the angular coordinates in (asymptotically) AdS$_5$ spacetime

In the papers I’ve seen with GR solutions in (asymptotically) AdS$_5$ spacetimes, when Boyer-Linquist-like coordinates $(t,r,\theta,\phi,\psi)$ are used, the ranges of the angular coordinates is as ...
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$AdS_3$ in complex coordinates

I am looking for a 2d manifold parametrized by $z$ and $\bar z$ such that $z \bar z = 1$. Now, to see what manifold it leads to I write $$z = \frac{x+iy}{1+iz}$$ so that by imposing $z\bar z = 1$, I ...
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Boundary terms in AdS space

Given the metric in AdS space $$ ds^2=\frac{r^2}{L^2}(-dt^2+d\vec{x}^2)+\frac{L^2}{r^2}dr^2 $$ I am trying to calculate the variation of the action of the KG equation in this metric. What would be ...
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KG on AdS space-time

In his TASI notes Oliver DeWolfe starts with the KG equation on the Poincaré patch metric $$ ds^2=\frac{r^2}{L^2}(-dt^2+dx^2)+\frac{L^2}{r^2}dr^2. $$ When we use the ansatz$$ \phi(r\rightarrow\infty,x,...
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I need help computing the effect of curvature on the FRW metric

Apparently there are different forms of the FLRW metric. I'm focusing on Anti-de Sitter space, so I'll just give the hyperbolic version of the function. $$ds^2=-c^2dt^2+a^2(t)\left[dr^2+R_0\space \...
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Deriving the expression for the AdS metric in global coordinates

I'm trying to work through the derivation of the coordinate expression for the AdS metric in global coordinates. I've found some resources for this, but they all leave out a few calculations, and when ...
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Superluminal speed in anti de sitter

This a bit of an elementary question, but I would like to understand how one correctly computes velocities in anti de sitter. It is well known that photons, traveling on null geodesics, will actually ...
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Confusion between Green function and solution of equation of motion in Witten's paper on holography and AdS

I was going through Witten's paper on AdS and holography , and am confused in section 2.4. He starts by considering a massless scalar action in Euclidean AdS spacetime, with a boundary value $\phi_0$. ...
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Criterion for a black hole in Anti-de Sitter background

Consider a Schwarzschild-Anti de Sitter (SAdS) metric $$ds^2=-(1-\frac{2M}{r}+ k\, r^2 )\, dt^2+\frac{dr^2}{1-\frac{2M}{r}+k \,r^2}+r^2 d\Omega_2^2, $$ with $M,k>0$. This solution has only ...
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Conformal properties of AdS space

My current research is connected with anti-de Sitter ṣpace, which is why I am interested in the following question. It is well known that the metric in Poincare patch is conformally equivalent to that ...
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Null Geodesics in Anti-de Sitter space time [closed]

Would anyone be able to explain how the step was taken in getting the final equation with $R \tan(t/R)$ I understand the steps before where we are finding the null geodesic equation for the AdS space ...
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Energy of a field configuration in General Relativity

I'm currently studying the article of Coleman and de Luccia about the bouncing configurations in an empty universe (DOI: https://doi.org/10.1103/PhysRevD.21.3305). In particular, they consider in the ...
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Symmetry v.s. isometry of Minkowski and AdS or dS spacetime

We know some nice spacetime have a lot of symmetries. It is said that Minkowski spacetime has $$ISO(d-1,1)/SO(d-1,1),$$ de Sitter spacetime has $$SO(d,1)/SO(d-1,1)$$ and anti-de Sitter spacetime ...
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Given in de Sitter space time is frozen on the horizon, can we say that in anti-de Sitter space time goes infinitely fast at the space boundary?

Particularly, in de Sitter space everything on the cosmic event horizon is redshifted, while in anti-de Sitter space everything on the horizon is blueshifted.
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How to find a coordinates transformation on $A\,\mathrm dS_2$?

I have the following 2D metrics (describing the $AdS_2$ spacetime), which are supposed to be the same in different coordinates: \begin{align} \mathrm ds^2 &= \mathrm dt^2 - \sin^2{\!\omega t} \, \...
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Which AdS/CFT correspondences have been found so far?

When I read about AdS/CFT correspondence, there always comes the most famous example of conjectured correspondence, which is the one between type IIB string theory (AdS side) and $\mathcal{N}=4$ ...
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How does AdS/CFT enact and not just be static geometry?

I understand the duality between the two regions of phase space (as Maldacena described it) that are Anti-de Sitter geometry and conformal field theory as an asymptotic grafting on of scale-invariant ...
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Why can AdS/CFT correspondence be applied to condensed matter systems when their space is not anti-deSitter?

The AdS/CFT correspondence postulates a duality between string theory of gravity and a CFT on an AdS background. This duality is employed in some condensed matter systems. I was wondering why it is ...
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The sphere $S^d$ is Euclidean space $E^d$ with infinity identified as a single point

I'm reading about anti de Sitter spacetime, and I found the following statement: $$ds^2 = \frac{1}{\cos^2 \psi} \big( -dt^2 + d\psi^2+ \sin^2 \psi d\Omega_{d-2}^2 \big).$$ Thus, the spatial sections ...
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$dS^d$ and $AdS^d$ are conformally equivalent

I have seen in the book by Zee (Einstein Gravity in a Nutshell) the following metric for $dS^4$: $ds^2 = \frac{1}{\cos^2 \tau} \big( - d\tau^2 + d\psi^2 + \sin^2 \psi \, d\Omega_2^2 \big) $, (Eq. IX....
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Geodesics of anti-de Sitter space

It is said that (p. 9), given the anti-de Sitter space $\text{AdS}_2$, let's say in the static coordinates $$ds^2 = -(1 + x^2) dt^2 + \frac{1}{(1+x^2)} dx^2$$ Every timelike geodesic will cross the ...
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What condition do global coordinates fulfil?

This may be a dumb or vague question: Is there any criterion that a metric tensor needs to fulfill such that coordinates it is expressed in can be called global. Or alternatively what is the ...
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BTZ black hole as an identification of $AdS_3$

I heard in a talk that a BTZ black hole can be obtained as an identification of the $AdS_3$ spacetime. Why exactly is the statement true? Also is it true that in (2+1)D all solutions of the Einstein ...
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Lorentz transformations in non-Euclidean geometries

I have an assessment/investigation coming up in my math class and I plan to investigate Lorentz transformations in geometries other than Euclidean such as spherical or hyperbolic. For spherical/polar, ...
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Metric of a Multipartite AdS-Schwarzschild Black Hole

In section 1 of Susskind's article (see https://arxiv.org/abs/1604.02589) on ER-EPR duality and its connection to the Everett and Copenhagen interpretation of quantum mechanics, he briefly studied ...
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Maximally symmetric spaces

In GR, what is the most precise definition of a maximally symmetric spacetime? Also, we study about the temporal boundary of dS space, and a spatial boundary of AdS space, but aren't these spaces ...
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Form of Light-Cone in pure $AdS_3$

There is a picture in the article of Harlow which (in particular) represents light cone in $AdS_3$. Note that point X has nonzero radial coordinate. If point X has zero radial coordinate it is quite ...
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Can a massive particle in AdS be dropped from the boundary?

My question revolves around the geodesics of massive point particles in fixed background AdS spacetime. Expressed in global coordinates $(\tau,\rho,\Omega_{i})$, the metric of $AdS_{d+1}$ (actually ...
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Symmetries of asymptotically AdS spacetimes

For asymptotically flat spacetimes, the group of symmetry tranformations of flat space, the Poincare group, is enhanced to the Bondi-Metzner-Sachs (BMS) group. Is there a similar enhancement for ...
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Representation theory of AdS and its classical field theory

I am looking for any resources which review the representation theory of the (Anti)-de Sitter group and its Lie algebra and its application to (classical) field theory. I am familiar with how this is ...
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Why isn't Anti de Sitter space taken seriously as a model of reality?

I asked a few questions here earlier regarding a physics model which could possibly point to Eternal Return, and was pointed towards Anti De Sitter space. Arguments in theories for Eternal Return ...
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Only the geodesic distance matters for maximally symmetric spacetimes

Any physical quantity $K(t,x,x')$ on a maximally symmetric spacetime only depends on the geodesic distance between the points $x$ and $x'$. Why is this so? N.B.: This statement is different from ...
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Symmetries of a radially-cut-off AdS$_3$ cylinder

The isometry group of the anti-de Sitter spacetime is $SO(d-1,2)$, which has a total of $\frac{1}{2}d(d+1)$ isometries. For the three-dimensional anti-de Sitter spacetime, these are $6$ isometries. ...
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Explicit form of the Poincare-AdS$_3$ geometry

The Poincare-AdS$_3$ geometry is given in the Wikipedia article on Anti-de Sitter space as $$ds^{2} = \frac{dr^{2}}{r^{2}} + r^{2}g_{\alpha\beta}dx^{\alpha}dx^{\beta}$$ $$=\frac{dr^{2}}{r^{2}} + r^{...
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Anti de Sitter space

While writing the metric for AdS Space, why are we starting with a five dimensional Flat space and embedding a hyperboloid in it? Does it have to do with the fact that the cosmological constant being ...
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Anti-De Sitter Space

Anti - De Sitter Space is the maximally symmetric solution to field equations with negative cosmological constant. The negative cosmological constant also shows that the spacetime has negative ...
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Does AdS$_3$ geometry have an angular momentum?

Consider the following hierarchy of masses for three-dimensional Einstein geometries with a locally AdS$_3$ metric: $$\text{global AdS}_3: M = -1/8G$$ $$\text{conical-defect-AdS}_3: -1/8G < M < ...
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Boundary conditions on conical deficit AdS geometry

The conical deficit global AdS$_3$ geometry is given by $$ds^{2} = - \cosh^{2}\rho\ dt^{2} + d\rho^{2} + \sinh^{2}\rho\ d\varphi^{2}, \qquad 0 \leq \varphi < 2\pi(1-4Gm'),$$ where $0 \leq 1-4Gm' &...
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Range of the radial coordinate for the Poincare-AdS$_3$ geometry

The metric of the Poincare-AdS$_3$ geometry is given in the Wikipedia article on the Poincare coordinates of AdS$_3$ geometry: $$ds^{2} = \alpha^{2}\left(\frac{du^{2}}{u^{2}} + u^{2}g_{\alpha\beta}dx^...
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Why Can't $AdS_5$ SUSY Extremal Black Holes be Large?

When we put the BPS condition and the extremality condition together on the most general black hole solution in $AdS_5$ (with minimally gauged supergravity), we get that the relation between the ...
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The AdS in AdS/CFT correspondence is really a class of spacetimes which asymptotes to a subclass of spacetimes with the same causal structure as AdS

On page 131 of these notes, a precise formulation of the AdS/CFT correspondence is given by the GKPW dictionary $$Z_{\text{grav}}[\phi_{0}^{i};\partial M] = \langle \exp \left( - \frac{1}{\hbar} \...
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Anti-de Sitter space in an embedding space

The Wikipedia page on anti-de Sitter space defines such a space as the hypersurface $$- X_{1}^{2}-X_{2}^{2} + \sum_{i=3}^{n+1}X_{i}^{2} = \frac{(n-1)(n-2)}{2\Lambda}$$ in an $n+1$-dimensional flat ...
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Boundary conditions due to local and global diffeomorphisms

Consider the following extract from page 2 of this paper. $AdS_3$ is the $SL(2, \mathbb{R})$ group manifold and accordingly has an $SL(2, \mathbb{R})_{L} \times SL(2, \mathbb{R})_{R}$ isometry ...
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Large $D$ limit of (Anti) de Sitter Space is Minkowskian Space?

As is well known, the solution of the vacuum Einstein equations with a non-zero cosmological constant, $G_{\mu\nu}+\Lambda g_{\mu\nu}=0$, is an asymptotically (anti) de Sitter space based on the sign ...
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Anti de Sitter and FLRW metrics

Perhaps this is a naive question, but I have been reading about conformal invariance and conformally related metrics and I would like to know if someone can clarify me some concepts on this. Anti de ...
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Deriving the Poincare patch from global coordinates in AdS$_{3}$

I have been reading Thomas Hartman's lecture notes on Quantum Gravity and Black Holes. In page 97, he derives (9.4), which is the metric of AdS$_{3}$ in global coordinates: $$ds^{2} = \ell^{2}(-\...