# Questions tagged [anti-de-sitter-spacetime]

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

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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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### 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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### 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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### Different AdS metrics in global coordinates

In David Tong's lecture notes I came across the folloing AdS metric in global coordinates \begin{equation} ds_3^2 = \left( \frac{dr^2}{\frac{r^2}{R^2} + 1 } - \left(\frac{r^2}{R^2} + 1 \right)dt^2 + ...
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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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### 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 ...
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### 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 ...
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### 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 ...
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### 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} ...
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### 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 ...
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### 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
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### 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 $\omega$ ...
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### 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 ...
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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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### 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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### 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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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 ...