Questions tagged [anti-de-sitter-spacetime]

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

Filter by
Sorted by
Tagged with
0
votes
0answers
40 views

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 ...
1
vote
1answer
66 views

Solving Schwarzian derivative differential equation in Hollowood & Kumar paper

I Was re-deriving Hollowood & Kumar paper (here is arXiv link of it) which is about Anti-De Sitter Black-Holes with JT Gravity, anyway I got a problem with solving a schwarzian derivative ...
2
votes
1answer
50 views

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 -...
0
votes
0answers
11 views

How to take the boundary limit in AdS

So I am reading these notes on AdS/CFT. In section 5, I am trying to understand the boundary of the AdS. They start with the metric in global coordinates \begin{equation} ds^2 = \frac{1}{\cosh(\frac{\...
0
votes
0answers
14 views

Embedding metric (projection) on AdS and Casimir operator

Recently, I am trying to follow up the appendix of arXiv:2106.10822, Embedding space formalism on $AdS_{d+1}$. Basically, I am trying to prove equation A.8 in the above figure. Let $X$ be a ...
2
votes
1answer
78 views

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 ...
12
votes
1answer
440 views

Role of the canonical ensemble and electric charge in AdS/CFT

If we consider a charged black hole in AdS spacetime, we can either do thermodynamics in the grand canonical or the canonical ensemble. In the former, we fix the electrostatic potential $\Phi=A_t(r=\...
3
votes
0answers
33 views

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 ...
7
votes
1answer
2k views

Geodesics in $\text{AdS}_3$

I'm having some trouble doing an easy computation with the $\text{AdS}$ space. I'm considering $\text{AdS}_3$ space with the Poincaré coordinates, so the metric reads $$ds^2 = \frac{R^2}{z^2}(dz^2 - ...
0
votes
1answer
51 views

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 ...
4
votes
0answers
68 views

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 (...
2
votes
0answers
57 views

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 ...
1
vote
0answers
42 views

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_{\...
0
votes
0answers
36 views

Are quadratic gravity's equations of motion just regular gravity with some minimal length?

So, I came to this while doing some calculations in quadratic gravity with the following action: \begin{equation} S = \int d^4x \sqrt{-g}\left[ \frac{1}{2}m^4+\frac{1}{6}m^2 R +\frac{1}{72}R^2+\frac{1}...
28
votes
2answers
10k views

Why are anti-de Sitter spaces so interesting when we believe the universe is expansionary?

Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, ...
0
votes
0answers
23 views

Breitenlohner-Freedman bound in AdS coupled theory

In this review of the AdS/CFT correspondence in section 2.2.2 we are given the scalar field equations of a quantum field theory in AdS spacetime. The energy-momentum tensor is given by $$ T_{\mu\nu}=2\...
1
vote
1answer
30 views

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\...
0
votes
1answer
133 views

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 ...
9
votes
1answer
2k views

Thermal AdS and the Hawking Page phase transition

I have some difficulty understanding the concept of pure thermal radiation, as described in Hawking and Page's paper on the Hawking-Page phase transition. The four-dimensional thermal AdS solution (...
0
votes
0answers
44 views

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 ...
1
vote
1answer
137 views

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 ...
7
votes
2answers
2k views

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 ...
1
vote
0answers
64 views

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 ...
0
votes
1answer
62 views

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 ...
1
vote
0answers
84 views

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 ...
2
votes
0answers
100 views

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, ...
2
votes
0answers
69 views

Misunderstanding of $\mathrm{AdS}_3$ spacetime

In my research I deal with $\mathrm{AdS}_3$ spacetime. It is convenient for me to use Poincare coordinates, which means that interval is given by $$ds^2 =\frac{1}{z^2}(-dt^2+dx^2+dz^2).\quad \tag{1}$$ ...
0
votes
1answer
43 views

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 $\...
0
votes
0answers
51 views

Mapping coordinates of $EAdS_2$ space

Three possible parametrizations of the Euclidean $AdS_2$ space ($H^2=EAdS_2$) are $$ds^2=\frac{1}{y^2}\left(dx^2+dy^2\right),\tag{1}\label{1}$$ $$ds^2=dr^2+\sinh^2r\,d\phi^2,\tag{2}\label{2}$$ $$ds^2=...
2
votes
1answer
194 views

Embed anti-de Sitter space in Minkowski or Euclidean space? (mathematical differences)

I'm a mathematician considering some geometry problems and generalizing them from spherical and hyperbolic manifolds. I wanted to try considering them in anti-de sitter geometry. Consider the manifold ...
1
vote
1answer
64 views

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 ...
0
votes
1answer
86 views

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 ...
8
votes
1answer
1k views

Classical theories and AdS/CFT

While editing the tag wiki for ads-cft, I initially wrote something on the lines of: The AdS/CFT correspondence is a special case of the holographic principle. It states that a gravitating theory in ...
2
votes
1answer
176 views

Killing Vectors in $AdS^2 \times S^2$

The metric for the product spacetime $AdS^2 \times S^2$ is given by $$ ds^2 = \dfrac{-dt^2 + dy^2}{y^2} + d\theta^2 + \sin^2 \theta \, d\phi^2.$$ Writing out the Killing equations yields a set of 10 ...
1
vote
1answer
70 views

Where is the observer in AdS-Schwarzschild coordinates?

for an AdS-Schwarzschild black hole in 4d, the metric is $$ ds^2 = -f(r)dt^2 + \frac{dr^2}{f(r)} + r^2d\Omega^2 $$ where $f(r) = 1 + r^2/l^2 - C/r$. $l$ is the AdS length scale and $C$ is some ...
0
votes
1answer
93 views

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 ...
2
votes
0answers
91 views

Euclidean anti-de Sitter space embedding

Let us take $\mathbb{R^{d+2}}$ with the cartesian coordinates $(X_0,\dots,X_{d+1})$ and the following metric : \begin{equation}\label{equ1} ds^2 = -dX^2_0-dX^2_{d+1}+\sum^d_{i=1}dX^2_i. \end{equation} ...
2
votes
1answer
183 views

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 ...
3
votes
1answer
123 views

Anti-de Sitter Spacetime Properties

I learned from reading nLab (https://ncatlab.org/nlab/show/anti+de+Sitter+spacetime) that the anti-de Sitter Spacetime of dimension $d$, $AdS_d$, is homeomorphic to $\mathbb{R}^{d-1} \times S^1$. I ...
1
vote
0answers
61 views

Why should fields in AdS spacetime vanish at infinity, but not in Minkowski spacetime?

I was watching the following lectures by Prof. Ashoke Sen. Between 39:00 and 56:00, he was solving the equation of classical field in the AdS global coordinates, and says that the values of $\omega$ ...
0
votes
0answers
52 views

Does AdS space-time have global translation symmetry?

I couldn't find any papers/articles addressing this particular issue. To elucidate, my question is the following, Question: Given the maximally symmetric nature of AdS space-time, we also have that it ...
1
vote
1answer
161 views

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 ...
0
votes
0answers
19 views

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 ...
1
vote
0answers
38 views

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 ...
2
votes
2answers
218 views

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 \...
2
votes
1answer
46 views

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,...
1
vote
1answer
54 views

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 ...
-1
votes
1answer
196 views

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 ...
0
votes
1answer
73 views

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 $\phi_0$. ...
2
votes
1answer
385 views

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 ...