Questions tagged [anti-de-sitter-spacetime]
Anti-de-Sitter (AdS) spacetime is a spacetime with a constant negative Ricci Scalar.
19
questions
4
votes
0
answers
55
views
Are de Sitter, Anti-de Sitter and Minkowski spaces spatially infinite?
I am not someone who has studied general relativity, however have recently developed an interest in it. From what I have seen online, de Sitter, Minkowski and Anti-de Sitter spaces are often compared ...
- 41
2
votes
0
answers
47
views
Robin conditions from action principle
Consider the Lagrangian density
$$L(\tilde{\phi}, \nabla \tilde{\phi}, \tilde{g}) = \tilde{g}^{\mu \nu} \nabla_{\mu} \tilde{\phi} \nabla_{\nu} \tilde{\phi} + \xi \tilde{R} \tilde{\phi}^2$$
with $\...
- 743
0
votes
0
answers
48
views
Conformal compactification of AdS spacetime
In this paper https://homes.psd.uchicago.edu/~ejmartin/course/JournalClub/Basic_AdS-CFT_JournalClub.pdf, page 2, the authors state "The boundary of the conformal compactified $AdS_{d+1}$ is ...
0
votes
1
answer
39
views
How do I prove that inversion and translation are an isometry in AdS?
I am using the AdS metric in Poincare coordinates, meaning $$ds^2 = \frac{R^2}{z^2}(dz^2 + d\vec{x}^2)$$
I want to prove why inversion $x^{\mu} = \dfrac{x'^{\mu}}{x'^2}$ and translation $x'^{\mu} =x^{\...
0
votes
0
answers
68
views
Killing Vectors AdS$_3$ (Solved)
I have been trying to understand the Killing vectors of AdS$_3$,i.e. Anti de Sitter in three dimension:
$$
ds^2 = dX^2 + dY^2 -dU^2 -dV^2
$$
In this case the generators are given by $J_{ab}=x_a \...
4
votes
0
answers
189
views
How does the bulk-to-boundary propagator transform under diffeomorphisms?
In AdS/CFT, the bulk-to-bulk propagator can be obtained as the limit of the bulk-to-bulk
propagator with one point approaching the boundary. For example in the scalar case
\begin{equation}
K_{\Delta}(...
- 98
0
votes
0
answers
21
views
Is it correct to claim that Hawking-Page phase transition is related to the breaking point at the Page-time?
In the evaporation process of a Black Hole in an AdS space we have a Hawking-Page phase transition. We know that such a phase transition can be exhibited by a singular behavior. At the other hand, ...
- 139
1
vote
0
answers
44
views
Global Hyperbolicity and Timelike Boundary
I am trying to understand and show that asymptotically Anti-de Sitter spacetimes are not globally hyperbolic.
Now, I have found papers that talk about global hyperbolic spacetimes with timelike ...
- 743
2
votes
1
answer
148
views
Negative $\Lambda$ FLRW spacetimes as infinite black holes?
Consider the Friedmann equation:
$$H^2+\frac{k}{a(t)^2} = \frac{\Lambda}{3}+\frac{8 \pi}{3}\rho$$
and set the parameters for dust in either flat euclidean or open hyperbolic spatial slices with a ...
- 125
2
votes
0
answers
115
views
Gravity dual of the string world-sheet CFT?
The AdS/CFT correspondence conjectures a duality between a $(D+1)$ dimensional gravity theory in asymptotic AdS spacetime with a $D$ dimensional conformal field theory. Is there any sense in asking ...
- 125
2
votes
0
answers
84
views
AdS compactification of Minkowski space
I am trying to understand the paper "Anti De Sitter Space And Holography" by E. Witten (cf. https://arxiv.org/abs/hep-th/9802150).
One of the first point it makes is that "Minkowski ...
3
votes
0
answers
38
views
Asymptotic AdS and coordinate change
I'm confused that boundary condition in 2d AdS spacetime. In two dimensions, we can write the metric in conformal gauge,
\begin{align}
ds^2=e^{2\omega(u,v)} dudv.
\end{align}
Suppose we impose the ...
- 89
1
vote
0
answers
36
views
Conformal mapping of Euclidean Schwarzschild AdS black hole
I have been trying to understand this for some time. given the Euclidean S-AdS black hole metric,
$$ ds^2 = f(r)d\tau^2 + \frac{1}{f(r)} dr^2 + r^2d\Omega^{2}_{D-2} $$
From what I understand this has ...
1
vote
1
answer
144
views
Need for boundary conditions in AdS space?
I am referencing to a passage on wikipedia's page about AdS space:
Because the conformal infinity of AdS is timelike, specifying the initial data on a spacelike hypersurface would not determine the ...
- 743
4
votes
1
answer
152
views
Penrose Diagram for AdS black hole
I am trying to construct the Penrose diagram of a black hole in AdS space. Now, I thought I was on a good track, my diagram looked like this:
The grey lines are the surfaces of constant $t$ and ...
- 743