Questions tagged [de-sitter-spacetime]
The de-sitter-spacetime tag has no usage guidance.
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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:
$$X^0=H^{-1}sinh(Ht)\sqrt{1-H^2r^2}$$
$$X^i=...
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$dS^d$ and $AdS^d$ are conformally equivalent
I have seen in the book by Zee (Einstein Gravity in a Nutshell) the following metric for $dS^4$:
$ds^2 = \frac{1}{\cos^2 \tau} \big( - d\tau^2 + d\psi^2 + \sin^2 \psi \, d\Omega_2^2 \big) $,
(Eq. IX....
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Why $dS^d \cong SO(d,1)/SO(d-1,1)$?
I have found a similar question, but there they give a seemingly rigorous proof, and what I am looking for is just an intuition.
I understand that $S^2 \cong SO(3)/SO(2)$: for every point in $S^2$ ...
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1answer
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Metric for 2D de Sitter?
What is the correct metric to use for two dimensional de Sitter? If one starts with the following metric, which looks similar to de Sitter in 4 dimensions:
$$ds^2 = -dt^2 + e^{2H t} dx^2,$$
one can ...
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1answer
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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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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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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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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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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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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 ...
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2answers
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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 ...
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1answer
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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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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} \,. $$
This metric ...
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1answer
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Holography on non-AdS spacetime
I have a question regarding AdS/CFT and what it teaches about our world. AdS/CFT if often treated as our best tool to explore quantum gravity, and people have worked very hard in trying to understand ...
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1answer
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Issues with de Sitter Space and Conformal Field Theory
As a de Sitter universe is more convenient for cosmology, what are the current issues with a dS/CFT type correspondence? Earlier work by Strominger, seemed promising but I haven't heard of additional ...
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Is the de Sitter Universe static?
In the book Tolman R.C. Relativity, thermodynamics, and cosmology (3pr., Oxford, 1949) I read that the de Sitter Universe is static as well as the Einstein Universe.
But the de Sitter Universe is ...
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Is the de Sitter Universe equivalent to the static Einstein Universe?
The de Sitter universe is a flat exponentially expanding universe with a cosmological constant $\Lambda$ and no matter.
Einstein's static universe also has a cosmological constant $\Lambda$ but it ...
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What coordinate system produces this particular form of the line element of de Sitter spacetime?
To save space, all the symbols and conventions are adopted from this Wikipedia article.
We know that the line element of $n$ dimensional de Sitter space in static coordinates is
$$ds^2=-\bigg(1-\...
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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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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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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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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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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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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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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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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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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 ...
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1answer
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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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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 ...
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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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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 ...
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2answers
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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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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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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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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 ...
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Static De Sitter Metric
For static dS metric we have
$$x_{0}=\sqrt{H^{-2}-r^{2}}\sinh(Ht)$$$$x_{1}=\sqrt{H^{-2}-r^{2}}\cosh(Ht)$$
and the metric can be written as
$$ds^{2}=-dx_{0}^{2}+dx^{2}_{1}+d\bar x$$ where the barred $...
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Definition of conformal time in de Sitter spacetime
I'm trying to follow the calculations in http://arxiv.org/abs/hep-th/0201158v2 The aim is to rederive the expressions (2.16), (2.17) for the power spectrum in de Sitter spacetime. In order to do so, ...
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Negative energy/mass bounds on de-Sitter spacetime
There exists a Positive Energy theorem for General Relativity in Anti-de Sitter and asymptotically flat spacetimes, but there is no equivalent theorem for de Sitter spacetimes
Question: Is there a ...
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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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Observers in (Schwarzschild-) de Sitter spacetime
In (pure) de Sitter spacetime, the cosmological horizon is said to be ‘observer dependent’. I imagine that as the observer always being in the center of that horizon. Another (spacelike separated) ...
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What is the gist of the equations on Alejandro Guijarro's “2/14” “Momentum” blackboard?
The artist Alejandro Guijarro has an exhibit of photographs of a variety of blackboards with physics equations, drawings and text on them, as covered at Quantum Chaos on Display in Top Physicists’ ...
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Wave equation for de Sitter invariant Green's functions
In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields:
$$(\square-m^2)G(x_1,x_2)=0 $$
can ...
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Geodesic distance in de Sitter space
Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space:
$$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$
where I set $H=1$ for ...
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Black hole temperature in an asymptotically de Sitter spacetime
I am trying to calculate the Hawking temperature of a Schwarzschild black hole in a spacetime which is asymptotically dS. Ignoring the 2-sphere, the metric is given by
$ds^2=\left(1-\frac{2M}{r}-\frac{...
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Are the cosmic horizons observer-specific?
It is known that all observers will agree on the position of the black hole event horizon. But what about the cosmic horizon of the de Sitter space? Can one say that the horizon of scientist1 is ...
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Can matter leave the cosmic horizon?
Cosmic horizon in the de Sitter space is a sphere, centered at the observer with finite radius where the red shift due to cosmic expansion becomes infinite.
Given that no information can be ...
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2answers
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Can Hubble red shift be interpreted as time dilation?
Can we interpret the de Sitter universe as a spherical cosmic horizon null surface of finite radius, centered at Earth, and containing the Hubble volume of space where time is dilated and radial ...
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Is it reasonable to assume that de Sitter temperature will stop growing when it reaches equilibrium with the temperature of CMB?
Is it reasonable to assume that de Sitter temperature will stop growing when it reaches equilibrium with the temperature of CMB?
Currently the de Sitter temperature (the temperature of the Universe's ...
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Some questions about spacetime topology, causality structures and other GR businesses
1) What are the exact conditions required for the canonical transformation? Most papers just assume away with global hyperbolicity, but is there a more general condition for it?
"Quantum gravity in ...
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de Sitter versus Minkowski QFT and cosmological constant
WMAP/Planck results confirm than we live in a de Sitter-like phase, i.e., a Universe with positive acceleration or positive cosmological constant! Therefore, I believe that a way to solve the ...
