Questions tagged [anti-de-sitter-spacetime]
Anti-de-Sitter (AdS) spacetime is a spacetime with a constant negative Ricci Scalar.
133
questions
0
votes
0answers
47 views
Mapping coordinates of $EAdS_2$ space
Three possible parametrizations of the Euclidean $AdS_2$ space ($H^2=EAdS_2$) are
$$ds^2=\frac{1}{y^2}\left(dx^2+dy^2\right),\tag{1}\label{1}$$
$$ds^2=dr^2+\sinh^2r\,d\phi^2,\tag{2}\label{2}$$
$$ds^2=...
0
votes
1answer
38 views
Isometries or Isometry direction of $AdS_5 \times S^5$
This is a consequent question with my previous question https://physics.stackexchange.com/q /610501/
I want to know the isometries (or isometry direction) of $AdS_5 \times S^5$. Usually, when we ...
0
votes
1answer
67 views
Metric form of $AdS_5 \times S^5$
I want to know the metric form of $AdS_5 \times S^5$.
I know there are two forms (maybe more?) Poincare patch and global patch.
And what is the difference between these two patches?
Can you state the ...
2
votes
1answer
86 views
Embed anti-de Sitter space in Minkowski or Euclidean space? (mathematical differences)
I'm a mathematician considering some geometry problems and generalizing them from spherical and hyperbolic manifolds. I wanted to try considering them in anti-de sitter geometry.
Consider the manifold ...
2
votes
1answer
55 views
Killing Vectors in $AdS^2 \times S^2$
The metric for the product spacetime $AdS^2 \times S^2$ is given by
$$ ds^2 = \dfrac{-dt^2 + dy^2}{y^2} + d\theta^2 + \sin^2 \theta \, d\phi^2.$$
Writing out the Killing equations yields a set of 10 ...
0
votes
0answers
35 views
Anti-deSitter space vacuum, null and weak energy condition
Anti-deSitter space is characterized by a negative cosmological constant.
This implies the energy momentum tensor =
$T_{\mu\nu} = -\lambda g_{\mu\nu}$, where $\lambda$ is taken positive.
This means ...
1
vote
1answer
53 views
Where is the observer in AdS-Schwarzschild coordinates?
for an AdS-Schwarzschild black hole in 4d, the metric is
$$
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
0answers
23 views
How to view thermal spacetime in “Minkowski” picture?
For things such as the Page-Hawking phase transition, we perform a Wick rotation, and consider the Free energy of the metric of a Black Hole in AdS (which has a periodic time to avoid conical ...
2
votes
0answers
49 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}
...
1
vote
0answers
39 views
Solving Schwarzian derivative differential equation in kumar paper
I Was re-driving 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 differential equation in 3....
0
votes
0answers
27 views
Isometries of $AdS_2$ space
So, in many places it is mentioned that isometries of pure $AdS_2$ space is the group $SL(2,R)$, defined by the transformation,
$t = (at+b)/(ct+d)$
where $ad-bc=1$.
Here, the boundary of $AdS_2$ is ...
2
votes
1answer
66 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
53 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
38 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
82 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 ...
0
votes
0answers
37 views
A question about the recent study that supports the Holographic Principle
First off, I agree with Susskind. There's no way to get around the Holographic universe. Maybe there will be one day, but each year it gets stronger and stronger. There's simply a limit to the ...
1
vote
1answer
92 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
13 views
What's the right way to include the characteristic length in the metric of a maximally symmetric space in General Relativity?
Given a maximally symmetric space with characteristic length $L$, I have seen different conventions when writting the factor explicitly in the metric, and I wonder if any interpretation is more ...
0
votes
0answers
18 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 ...
0
votes
0answers
25 views
$AdS_3$ in complex coordinates
I am looking for a 2d manifold parametrized by $z$ and $\bar z$ such that $z \bar z = 1$. Now, to see what manifold it leads to I write $$z = \frac{x+iy}{1+iz}$$ so that by imposing $z\bar z = 1$, I ...
1
vote
0answers
30 views
Boundary terms in AdS space
Given the metric in AdS space
$$
ds^2=\frac{r^2}{L^2}(-dt^2+d\vec{x}^2)+\frac{L^2}{r^2}dr^2
$$
I am trying to calculate the variation of the action of the KG equation in this metric.
What would be ...
2
votes
1answer
43 views
KG on AdS space-time
In his TASI notes Oliver DeWolfe starts with the KG equation on the Poincaré patch metric
$$
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,...
2
votes
2answers
144 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.
$$ds^2=-c^2dt^2+a^2(t)\left[dr^2+R_0\space \...
0
votes
0answers
59 views
Deriving the expression for the AdS metric in global coordinates
I'm trying to work through the derivation of the coordinate expression for the AdS metric in global coordinates. I've found some resources for this, but they all leave out a few calculations, and when ...
1
vote
1answer
40 views
Superluminal speed in anti de sitter
This a bit of an elementary question, but I would like to understand how one correctly computes velocities in anti de sitter. It is well known that photons, traveling on null geodesics, will actually ...
0
votes
1answer
63 views
Confusion between Green function and solution of equation of motion in Witten's paper on holography and AdS
I was going through Witten's paper on AdS and holography , and am confused in section 2.4. He starts by considering a massless scalar action in Euclidean AdS spacetime, with a boundary value $\phi_0$. ...
-1
votes
1answer
187 views
Criterion for a black hole in Anti-de Sitter background
Consider a Schwarzschild-Anti de Sitter (SAdS) metric
$$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, $$
with $M,k>0$. This solution has only ...
2
votes
1answer
365 views
Conformal properties of AdS space
My current research is connected with anti-de Sitter ṣpace, which is why I am interested in the following question. It is well known that the metric in Poincare patch is conformally equivalent to that ...
1
vote
1answer
136 views
Null Geodesics in Anti-de Sitter space time [closed]
Would anyone be able to explain how the step was taken in getting the final equation with $R \tan(t/R)$
I understand the steps before where we are finding the null geodesic equation for the AdS space ...
2
votes
1answer
89 views
Symmetry v.s. isometry of Minkowski and AdS or dS spacetime
We know some nice spacetime have a lot of symmetries. It is said that
Minkowski spacetime has
$$ISO(d-1,1)/SO(d-1,1),$$
de Sitter spacetime has
$$SO(d,1)/SO(d-1,1)$$ and
anti-de Sitter spacetime ...
1
vote
0answers
43 views
Given in de Sitter space time is frozen on the horizon, can we say that in anti-de Sitter space time goes infinitely fast at the space boundary?
Particularly, in de Sitter space everything on the cosmic event horizon is redshifted, while in anti-de Sitter space everything on the horizon is blueshifted.
0
votes
1answer
57 views
How to find a coordinates transformation on $A\,\mathrm dS_2$?
I have the following 2D metrics (describing the $AdS_2$ spacetime), which are supposed to be the same in different coordinates:
\begin{align}
\mathrm ds^2 &= \mathrm dt^2 - \sin^2{\!\omega t} \, \...
5
votes
0answers
122 views
Which AdS/CFT correspondences have been found so far?
When I read about AdS/CFT correspondence, there always comes the most famous example of conjectured correspondence, which is the one between type IIB string theory (AdS side) and $\mathcal{N}=4$ ...
0
votes
0answers
71 views
How does AdS/CFT enact and not just be static geometry?
I understand the duality between the two regions of phase space (as Maldacena described it) that are Anti-de Sitter geometry and conformal field theory as an asymptotic grafting on of scale-invariant ...
2
votes
1answer
211 views
Why can AdS/CFT correspondence be applied to condensed matter systems when their space is not anti-deSitter?
The AdS/CFT correspondence postulates a duality between string theory of gravity and a CFT on an AdS background. This duality is employed in some condensed matter systems. I was wondering why it is ...
4
votes
1answer
124 views
The sphere $S^d$ is Euclidean space $E^d$ with infinity identified as a single point
I'm reading about anti de Sitter spacetime, and I found the following statement:
$$ds^2 = \frac{1}{\cos^2 \psi} \big( -dt^2 + d\psi^2+ \sin^2 \psi d\Omega_{d-2}^2 \big).$$
Thus, the spatial sections ...
0
votes
1answer
62 views
$dS^d$ and $AdS^d$ are conformally equivalent
I have seen in the book by Zee (Einstein Gravity in a Nutshell) the following metric for $dS^4$:
$ds^2 = \frac{1}{\cos^2 \tau} \big( - d\tau^2 + d\psi^2 + \sin^2 \psi \, d\Omega_2^2 \big) $,
(Eq. IX....
6
votes
2answers
961 views
Geodesics of anti-de Sitter space
It is said that (p. 9), given the anti-de Sitter space $\text{AdS}_2$, let's say in the static coordinates
$$ds^2 = -(1 + x^2) dt^2 + \frac{1}{(1+x^2)} dx^2$$
Every timelike geodesic will cross the ...
3
votes
2answers
94 views
What condition do global coordinates fulfil?
This may be a dumb or vague question:
Is there any criterion that a metric tensor needs to fulfill such that coordinates it is expressed in can be called global. Or alternatively what is the ...
7
votes
1answer
376 views
BTZ black hole as an identification of $AdS_3$
I heard in a talk that a BTZ black hole can be obtained as an identification of the $AdS_3$ spacetime. Why exactly is the statement true?
Also is it true that in (2+1)D all solutions of the Einstein ...
1
vote
1answer
108 views
Lorentz transformations in non-Euclidean geometries
I have an assessment/investigation coming up in my math class and I plan to investigate Lorentz transformations in geometries other than Euclidean such as spherical or hyperbolic. For spherical/polar, ...
2
votes
1answer
88 views
Metric of a Multipartite AdS-Schwarzschild Black Hole
In section 1 of Susskind's article (see https://arxiv.org/abs/1604.02589) on ER-EPR duality and its connection to the Everett and Copenhagen interpretation of quantum mechanics, he briefly studied ...
1
vote
2answers
2k views
Maximally symmetric spaces
In GR, what is the most precise definition of a maximally symmetric spacetime?
Also, we study about the temporal boundary of dS space, and a spatial boundary of AdS space, but aren't these spaces ...
1
vote
1answer
100 views
Form of Light-Cone in pure $AdS_3$
There is a picture in the article of Harlow which (in particular) represents light cone in $AdS_3$. Note that point X has nonzero radial coordinate.
If point X has zero radial coordinate it is quite ...
2
votes
0answers
89 views
Can a massive particle in AdS be dropped from the boundary?
My question revolves around the geodesics of massive point particles in fixed background AdS spacetime. Expressed in global coordinates $(\tau,\rho,\Omega_{i})$, the metric of $AdS_{d+1}$ (actually ...
2
votes
0answers
84 views
Symmetries of asymptotically AdS spacetimes
For asymptotically flat spacetimes, the group of symmetry tranformations of flat space, the Poincare group, is enhanced to the Bondi-Metzner-Sachs (BMS) group. Is there a similar enhancement for ...
1
vote
0answers
57 views
Representation theory of AdS and its classical field theory
I am looking for any resources which review the representation theory of the (Anti)-de Sitter group and its Lie algebra and its application to (classical) field theory. I am familiar with how this is ...
4
votes
3answers
2k views
Why isn't Anti de Sitter space taken seriously as a model of reality?
I asked a few questions here earlier regarding a physics model which could possibly point to Eternal Return, and was pointed towards Anti De Sitter space.
Arguments in theories for Eternal Return
...
3
votes
0answers
86 views
Only the geodesic distance matters for maximally symmetric spacetimes
Any physical quantity $K(t,x,x')$ on a maximally symmetric spacetime only depends on the geodesic distance between the points $x$ and $x'$.
Why is this so?
N.B.:
This statement is different from ...
0
votes
0answers
49 views
Symmetries of a radially-cut-off AdS$_3$ cylinder
The isometry group of the anti-de Sitter spacetime is $SO(d-1,2)$, which has a total of $\frac{1}{2}d(d+1)$ isometries.
For the three-dimensional anti-de Sitter spacetime, these are $6$ isometries.
...