# Tagged Questions

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

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### Timelike Boundary

I was reading in a paper (see 1st paragraph of introduction section in http://arxiv.org/pdf/1510.00709.pdf) that in AdS space, waves can reach the boundary in finite time and, since said boundary is ...
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### Why can only asymptotically flat and AdS black hole have the thermodynamics? What's about asymptoticaly dS black hole?

Almost all advanced GR textbooks will have the content of black hole thermodynamics for asymptotically flat black hole. And this paper solve the asymptotically AdS (Anti-de Sitter) black hole http://...
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### Stability condition for AdS background (when gravity coupled to matter fields)

In finding the stability condition for AdS background (when gravity coupled to matter fields), why the conserved energy should be positive?
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### Quasilocal stress tensor

I have been reading through the paper hep-th/9902121 and have a few questions about the first five lines of the introduction: 1) "In a generally covariant theory, it is unnatural to assign a local ...
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### How does one show that asymptotically $AdS_3$ spacetimes are locally $AdS_3$?

Time and again I keep reading that any asymptotic $AdS_3$ spacetime is locally isomorphic to $AdS_3$. I tried to find proof of this by analyzing the Riemann tensor $R_{\rho\sigma\mu\nu}$ in Ricci ...
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### Sign convention with the $AdS$ metric

One would say that $AdS_n$ satisfies the equations for the scalar curvature (R) and Ricci tensor ($R_{\mu \nu}$), $R = - \frac{n(n-1)}{L^2}$ and $R_{ab} = - \frac{n-1}{L^2}g_{ab}$. But do the signs ...
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### Warped AdS${}_3$ and symmetry breaking

In this article it is explained how on can (in suitable coordinate basis) get a so called warped AdS${}_3$ black hole, by introducing a warping factor. The original metric in 'Euler coordinates' for ...
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### Generalisations of AdS/CFT with string theory on both sides

From my previous post, I found out from the comments that there are various generalisations of AdS/CFT with different things replacing the CFT on the RHS; such as AdS/CMT, AdS/QCD, and also with ...
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### Getting the AdS metric from maximally symmetric spaces

I am familiar with the way we derive the form of the FRW metric by just using the fact that we have a maximally symmetric space i.e the universe is homogeneous and isotropic in spatial coordinates. ...
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### BTZ Black holes

I computed the two point function for two scalar fields in BTZ black hole that is defined as a local $AdS_3$ space time with discrete identification, as defined in many papers. Referring to this paper,...
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### Radiation collapse to black hole

I want to find the temperature at which radiation in AdS will collapse to form a black hole. I have even found a reference that gives the answer but I cannot understand it: http://srv2.fis.puc.cl/~...
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On p77 of these lecture notes (http://arxiv.org/pdf/0712.0689v2.pdf), we are asked to check that a light ray takes infinitely long to reach the centre of AdS. 1, Why doesn't the Penrose diagram for ...
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### Solution of Dirichlet problem for scalar field in Ads

I am reading "Anti de Sitter space and holography" by Witten. In this article he derives the two-point function for CFT from theADS/CFT correspondence for a massless scalar field living in the bulk. ...
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### Euclidean AdS space in Poincaré coordinates

I have read anti-de Sitter (AdS) space and its Euclidean version both in Global and Poincaré coordinates. For Lorentzian case it is clear how one Poincaré patch cover only one half of the whole AdS ...
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### Questions about Type HE Matrix String Theory

I was reading the heterotic string section of this thesis desertation by Luboš Motl, since I think I now understand the Type IIA Matrix String Theory. The only thing I knew about Type HE Matrix ...
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### AdS boundary global vs Poincare'

Is the global boundary of AdS the same of the boundary written in Poincare' coordinates?
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### Volume form of the AdS_{4} Space

Regarding the unit radius $AdS_{4}$ space, the metric in global coordinates, is given by: $$ds^{2}_{AdS_{4}}=\frac{1}{\cos^{2}{\rho}}[dt^{2}-d\rho^{2}-\sin^{2}\rho d\Omega_{2}^{2}]$$ where d\...
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### Anti de-Sitter Geodesics

Timelike geodesics in anti de-Sitter space cannot reach infinity. I believe this has something to do with Clairaut's relation. I'm pretty sure it's true though as the analogy with conservation of ...
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### de Sitter reviews?

I'm very interested in learning more about de Sitter and anti-de Sitter spaces and their applications in GR and cosmology. Can anyone recommend favorite review articles -- or, more likely, a series ...
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### Anti de Sitter Motion without matter

I've read that a non zero cosmological constant can lead to "motion without matter" in vacuum spacetimes such as AdS. Initially I didn't understand what the significance of this statement was since I ...
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### Motion without matter

Suppose you have a vacuum spacetime with non zero cosmological constant then you can show that two test particles will move toward each other or apart depending on whether it is negative or positive (...
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I've been reading some notes ("Anti-de Sitter space" by Bengtsson) on anti-de Sitter space. It is shown in equation 152 that timelike observers at fixed radial distance from the origin experience a ...
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### Geodesics on dS and AdS

I have been reading through the following paper "The dS and AdS Sightseeing Tour" (http://www.bourbaphy.fr/moschella.pdf) but I am not clear about why geodesics appear as hyperbola in the dS case (see ...
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### What is the status of the area theorem in AdS?

The area theorem, by Hawking (in "Gravitational Radiation from Colliding Black Holes", also found in Wald), states that the area of an event horizon cannot decrease with time. As I understand, there ...