Questions tagged [de-sitter-spacetime]
The de-sitter-spacetime tag has no usage guidance.
77
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What is the Komar mass of the de-Sitter spacetime?
The Komar mass of some spacetime is defined as an integral (volume or surface, depending on its formulation): https://en.wikipedia.org/wiki/Komar_mass
The de-Sitter metric in static coordinates is ($\...
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0answers
71 views
Negative temperature of the de-Sitter horizon?
I'm considering the $4D$ de-Sitter spacetime, in static coordinates (I'm using $c = 1$ and $k_{\text{B}} = 1$):
\begin{equation}\tag{1}
ds^2 = (1 - \frac{\Lambda}{3} \, r^2) \, dt^2 - \frac{1}{1 - \...
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62 views
Entropy of de-Sitter spacetime and the $10^{120}$ vacuum discrepency
While doing some lazy calculations, I came across a curiosity that I'm unable to interpret. It is well known that the cosmological constant $\Lambda \sim 10^{-52}~\mathrm{m^{-2}}$ is usually ...
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19 views
dS/CFT in a positive curvature universe
Since Maldacena ground breaking theoretical discovery, have there been any succesfull efforts to try to transpose the AdS/CFT duality to our universe (not an AdS)?
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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 ...
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1answer
23 views
In de Sitter space, does the cosmic horizon change its shape for fast-moving observer?
If an observer moves at a speed close to the speed of light, will the horizon deviate from spherical shape?
If no, will it be the same horizon as for stationary observer (at the same position)?
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30 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.
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Gravitational contribution to the action for Coleman-de Luccia instanton?
In the Coleman-de Luccia calculation of the transition rate from one de Sitter minimum to another, the action for the scalar field $\phi(\xi)$ and Euclidean radius $\rho(\xi)$ is
$S_E = 2\pi^2 \int \...
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1answer
77 views
Minkowski space vs De Sitter Space
Can you explain to a layman the differences between the former two?
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1answer
84 views
Does an observer inside a black hole experience the de Sitter metric?
My question has emerged, because of the following similarities between the metric an observer experiences in the Schwartzschild space being under the Schwartzschild radius and an observer in the de ...
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23 views
Is there a de Sitter or FRW collapse solution for black holes, similar to the Oppenheimer-Snyder-collapse?
I know the Oppenheimer-Snyder-solution and the formation of the black hole event horizon during the collapse.
Is there a similar solution for a dynamical collapse, embedded in asymptotic de Sitter ...
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56 views
How accurate is the De Sitter solution of the Einstein field equations of general relativity?
The De sitter solution models the universe as spatially flat, neglecting ordinary matter, such that it is dominated by the cosmological constant. The cosmological constant notion arguably suggests the ...
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0answers
32 views
How is deSitter group tranformations different from poincare group transformations
In QFT, we have studies Poincare group of massive and massless particles. Is the deSitter group also useful to study such things? What exactly is the main role of this group in QFT?
I just know the ...
2
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4answers
194 views
What would happen to de Sitter universe if the cosmological constant disappears?
De sitter universe is dominated by a cosmological constant (devoid of matter and radiation), corresponding to dark energy in the far future or the inflaton field in the early
universe, leading to an ...
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25 views
2D deSitter conserved charges
For $1+1$-dimensional dS spacetime, the metric takes the form (in comoving coordinates) $$\mathrm{d}s^2=\left(\mathrm{d}x^0\right)^2-e^{2Hx^0}\left(\mathrm{d}x^1\right)^2.$$ I want to find the ...
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48 views
deSitter spacetime metric and curvature
I have to compute the metric of an hyperboloid given by $-(X^0)^2+(X^1)^2+(X^2)^2+(X^3)^2=H^{-2}$ in 5D Minkowski spacetime using the following coordinates:
$$X^0=H^{-1}\sinh(Ht)\sqrt{1-H^2r^2}$$
$$X^...
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1answer
58 views
$dS^d$ and $AdS^d$ are conformally equivalent
I have seen in the book by Zee (Einstein Gravity in a Nutshell) the following metric for $dS^4$:
$ds^2 = \frac{1}{\cos^2 \tau} \big( - d\tau^2 + d\psi^2 + \sin^2 \psi \, d\Omega_2^2 \big) $,
(Eq. IX....
2
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1answer
73 views
Why $dS^d \cong SO(d,1)/SO(d-1,1)$?
I have found a similar question, but there they give a seemingly rigorous proof, and what I am looking for is just an intuition.
I understand that $S^2 \cong SO(3)/SO(2)$: for every point in $S^2$ ...
3
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1answer
318 views
Metric for 2D de Sitter?
What is the correct metric to use for two dimensional de Sitter? If one starts with the following metric, which looks similar to de Sitter in 4 dimensions:
$$ds^2 = -dt^2 + e^{2H t} dx^2,$$
one can ...
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1answer
94 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, ...
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0answers
93 views
Strings 2018 takeaways [closed]
What are the main takeaways from the Strings 2018 conference? What are the main announcements, discoveries or directions emerging from this event?
To my knowledge, one is the result by Vafa and ...
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0answers
110 views
If the Schwarzschild radius of the universe is bigger than the universe, how come the universe didn't collapse into a black hole? [duplicate]
According to this answer, the Schwarzschild radius of the universe is about 3 times the radius of the universe. According to the Newtonian theory of gravity, inside any sphere of a given density, the ...
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2answers
1k views
Why is our physical Universe a de Sitter space?
Wikipedia says,
When $n=4$ (3 space dimensions plus time), it is (the de Sitter space) a cosmological model for the physical universe; see de Sitter universe.
It appears to me that the statement ...
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1answer
291 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 ...
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0answers
61 views
De sitter spacetime and co-ordinates
I was recently looking at de - Sitter spacetime and I relaized that there are many different parameterizations possible, each of which has it's own advantages.
Can someone help me out and list the ...
4
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2answers
555 views
Can String Theory really fail to contain a de Sitter vacua?
I was reading a post earlier from Peter Woit's Not Even Wrong blog and came across the following reference to the paper "What if string theory has no de Sitter vacua?" by Ulf H. Danielsson, Thomas Van ...
2
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1answer
39 views
Can a De Sitter universe have a detectable rotation?
In De Sitter relativity, the cosmological constant becomes a geometric term with the dimensions of radius, and the universe becomes a pseudo-sphere.
Is it meaningful to speak of intrinsic rotation of ...
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2answers
236 views
Is the dynamics of spacetime observer-dependent?
Consider de Sitter spacetime in static coordinates:
$$ ds^2 = \Big(1- (H_\Lambda r)^2 \Big) dt^2 - \frac{dr^2}{1- (H_\Lambda r)^2} -r^2 d\Omega^2, \qquad r\lt H_\Lambda^{-1} \,. $$
This metric ...
5
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1answer
221 views
Holography on non-AdS spacetime
I have a question regarding AdS/CFT and what it teaches about our world. AdS/CFT if often treated as our best tool to explore quantum gravity, and people have worked very hard in trying to understand ...
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1answer
218 views
Issues with de Sitter Space and Conformal Field Theory
As a de Sitter universe is more convenient for cosmology, what are the current issues with a dS/CFT type correspondence? Earlier work by Strominger, seemed promising but I haven't heard of additional ...
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2answers
1k views
Is the de Sitter Universe static?
In the book Tolman R.C. Relativity, thermodynamics, and cosmology (3pr., Oxford, 1949) I read that the de Sitter Universe is static as well as the Einstein Universe.
But the de Sitter Universe is ...
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1answer
400 views
Is the de Sitter Universe equivalent to the static Einstein Universe?
The de Sitter universe is a flat exponentially expanding universe with a cosmological constant $\Lambda$ and no matter.
Einstein's static universe also has a cosmological constant $\Lambda$ but it ...
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0answers
39 views
What coordinate system produces this particular form of the line element of de Sitter spacetime?
To save space, all the symbols and conventions are adopted from this Wikipedia article.
We know that the line element of $n$ dimensional de Sitter space in static coordinates is
$$ds^2=-\bigg(1-\...
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1answer
902 views
Is de Sitter space with non-zero curvature an acceptable model for the universe?
On wikipedia I can find that a de Sitter-space has maximal symmetry and a constant curvature. Recently the interest of de Sitter spaces has increased as it could serve as a model for the universe, an ...
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41 views
Is there a homogeneous $\Lambda$-vacuum spacetime with spatial topology $\mathbb{R}^2\times S^1$?
This question is about homogeneous $\Lambda$-vacuum spacetimes. The unique isotropic solution is de Sitter space, which has the spatial topology of $\mathbb{R}^3$. There is the Kantowski-Sachs metric,
...
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0answers
107 views
Does the curvature parameter $k$ change with coordinate choice (de Sitter spacetime)?
The de Sitter spacetime can be derived from the vacuum Friedmann equations given a choice of $k=0$, where $k$ defines the spatial curvature of the spacetime. The resulting metric in $(t,x,y,z)$ is ...
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91 views
de-Sitter spacetimes
In classical textbooks for GR, Schwarzschild and Kerr spacetimes are adequately described. In which books or articles, it is mostly believed that Reissner-Nordstrom, Kerr-Newman, Schwarzschild-de ...
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3answers
186 views
Large $D$ limit of (Anti) de Sitter Space is Minkowskian Space?
As is well known, the solution of the vacuum Einstein equations with a non-zero cosmological constant, $G_{\mu\nu}+\Lambda g_{\mu\nu}=0$, is an asymptotically (anti) de Sitter space based on the sign ...
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0answers
2k views
A Universal Upper Limit on Mass Within a Radius $R$?
Since the universe has a positive cosmological constant, there is an upper limit on the mass of the black holes as evident from the so-called Schwarzschild-de Sitter metric:
$ds^2 = -f(r)dt^2 + \...
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1answer
144 views
How does one write a three dimensional de Sitter space as the quotient $SL(2, C)/SL(2, R)$?
In arXiv:hep-th/0110108 the $(2+1)-$dimensional de Sitter space is represented as a quotient space of $SL(2, C)/SL(2, \mathbb{R})$. I couldn't understand how, both mathematically and intuitively, is ...
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1answer
159 views
Totally geodesic spacelike surfaces in de Sitter space
Let $S^2_1$ be the de Sitter space $$\{x:\langle x,x\rangle=x_0^2-x_1^2-x_2^2-x_3^2=-1\}$$ in Minkowski space $\mathbb {R}^3_1$ with $ds^2=dx_0^2-dx_1^2-dx_2^2-dx_3^2$. Is it true that for each pair ...
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1answer
654 views
What are the de Sitter Killing vectors?
I'm trying to find the Killing vectors for de Sitter space using global coordinates, i.e. the spherical foliation. In the end, I want to know how to perform a boost on the 1+1 and 3+1 de Sitter ...
6
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1answer
340 views
Entropy of the de Sitter cosmological horizon
For an eternal dS universe, the entropy of an observer in the static patch goes as the area of the horizon which for 3+1 D goes as $S_H = \frac{Area_{H}}{4} \sim H^{-2}$, as given by Gibbons & ...
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190 views
Lapse Function and Shift Vector in Minkowski and de Sitter
I'd like to find the lapse function and shift vector in 1+1 Minkowski as well as 1+1 de Sitter (flat foliation) for a region foliated this way:
The $y$-axis represents time while the x-axis ...
2
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1answer
193 views
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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3answers
1k views
If the expansion of the Universe accelerates, why its horizon does not shrink?
In de Sitter (expanding) universe to which our universe asymptotically approaches, the higher the rate of space expansion, the smaller the radius of the cosmic horizon. Why then our universe is ...
6
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2answers
241 views
Are orbits possible in de sitter space?
Since the de sitter space has constant positive curvature does that mean that objects can't orbit around other objects?
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1answer
300 views
Why $C_{abcd}C^{abcd}$ in de Sitter–Schwarzschild metric doesn't depend on $\Lambda$
With the de Sitter–Schwarzschild metric:
$$ds^2=-\left(1-\frac{2M}{r}-\frac{\Lambda r^2}{3}\right)dt^2+\left(1-\frac{2M}{r}-\frac{\Lambda r^2}{3}\right)^{-1}dr^2+r^2d\theta+r^2\sin^2\theta d\phi$$
I ...
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188 views
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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281 views
How to find de Sitter and almost de Sitter solutions in (super)string theory
From Cosmology, we have learned that we live in an almost de Sitter (positively accelerated!) Universe. It seems that dS space solutions in superstring/theory are problematic and there are some no-go ...
