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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Basically, I want to know how one can see the $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ symmetry of AdS$_3$ explicitly. AdS$_3$ can be defined as hyperboloid in $\mathbb{R}^{2,2}$ as $$X_{-1}^2+X_0^... 0answers 33 views BTZ Black holes I computed the two point function for two scalar fields in BTZ black hole that is defined as a local AdS_3 space time with discrete identification, as defined in many papers. Referring to this paper,... 0answers 100 views Question on E_8 and twistor space [closed] The Kahler 4 form constructed from two-forms \{\alpha, \beta\} \in H^2(M,\mathbb Z), and M a 4-manifold, is induced by \alpha\wedge\beta with the map H^2(M, \mathbb Z)\otimes H^2(M, \mathbb ... 0answers 28 views Volume form of the AdS_{4} Space Regarding the unit radius AdS_{4} space, the metric in global coordinates, is given by:$$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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Is the global boundary of AdS the same of the boundary written in Poincare' coordinates?
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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, ...
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Changing vector basis in AdS$_3$

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
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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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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 (...
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Mass of empty AdS$_5$

Five dimensional empty AdS$_5$ space has mass $$E = \frac{3 \pi \ell^2}{32 G}.$$ Is the above equation correct? Let's do some dimensional analysis to confirm. In natural units, in 5 dimensions ...
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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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When I was editing the Physics.SE 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 ...
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I am having difficulty of finding more basic information on warped geometries. All the standard textbooks are not covering it. In the wiki article it's only said that warped geometry is the one which ...
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In AdS/CFT papers the action of the SO(D,2) symmetry is usually given at the boundary where the transformations are just the conformal transformations (Poincare, scaling and special) for D+1 ...
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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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Why is spacetime near a quantum black hole approximately AdS?

In this link, one of the answers contains the statement If you examine the space-time near a finite area quantum black hole, you will see an approximate AdS space. Presumably "approximate" ...
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Getting diffeomorphisms from boundary conditions in $AdS_3$

As usual I'm asking a question about boundary conditions for AdS${}_3$, based on the thesis by Porfyriadis. He is solving equations $\mathcal{L}_\xi g_{\mu\nu}$ for AdS${}_3$ metric, with a given ...
How does one see that that the Euclidean AdS is the same as the hyperbolic space at the same dimension ie $EAdS_n = \mathbb{H}_n = SO_0(n,1)/SO(n)$? Or is this to be seen as the definition of ...