Questions tagged [de-sitter-spacetime]

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The extreme dS black holes in 5 dimensions

In the paper https://arxiv.org/abs/hep-th/0401192, we have a $f(r)$ in Eq(6). $$f(r)=1-(\Lambda/3)r^2-M/r^{(D-3)}+Q^2/r^{2D-6}$$ In 5 dimension $f(r)$ is $$f(r)=1-(\Lambda/3)r^2-M/r^2+Q^2/r^{4}$$ For ...
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Is there an expression for a black hole in global deSitter coordinates?

The usual deSitter-Schwartzchild black hole is expressed in terms of the static patch, is there a coordinate patch and metric that describes global deSitter with a black hole?
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On the nature of Earth's past light cone in an expanding universe

As our telescopes look further and further from Earth, they are observing older and older cosmic phenomena. But if you look far enough to see something that occurred "shortly" after the big ...
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Time evolution of point density in de-Sitter space

If I were to instantiate a 3D de-Sitter universe filled with evenly-spaced, massless points, how would I calculate the proportion of points that remain within the event horizon of an arbitrary point ...
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EM tensor in de Sitter spacetime

The energy momentum tensor for a particle in Minkowski space at position $\textbf{r}_A$ is given by: $$T^{\mu \nu} = \frac{p^{\mu}p^{\nu}}{E/c^2}\delta(\textbf{r} - \textbf{r}_A)$$ I want to ...
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Solution of Einstein's field equation for local energy density

If there is a uniform positive energy density present in a patch of space-time, what would be the metric describing the patch? a de-Sitter patch? What would be the gravitational potential felt by a ...
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What is the topology of a de Sitter spacetime with multiple timelike dimensions?

(I believe that) de Sitter space is the only maximally symmetric Lorentzian spacetime, and that for $n$ spacetime dimensions, it has the hypercylindrical topology $\mathbb{R} \times S^{n-1}$. This is ...
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Has DeSitter radiation been observed or experimentally verified?

I found an interesting article by Paul Davies (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.30.737) which involves radiation emmited by DeSitter horizons. But is it a fact that this ...
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Cosmic expansion from De-Sitter global coordinates metric

Can we show cosmic expansion from this dS metric? \begin{equation} ds^{2} = -d\tau^{2} + R^{2}\cosh^{2}(\tau/R) d\Omega^{2}_{3} \end{equation} I understand that in this background, matter can be set ...
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Might the tiny Hawking radiation from our cosmic event horizon (CEH) be additive, since my CEH is not your CEH?

Concerning our cosmic event horizon, an interesting question arises from the seemingly innocent statement, "My cosmic event horizon is not your cosmic event horizon." Ie: Since 'you' and 'I'...
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Supergravity in our universe of accelerated expansion

In "On supergravity theories, after ~40 years" (Jean-Pierre Derendinger) presented on DISCRETE 2014" it is said (p.16) that a positive cosmological constant is not compatible with ...
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Notation for the metric of $\rm dS_4$ and/or $\rm AdS_4$

4D de Sitter and anti-de Sitter spaces may have their metrics inferred from the induced metric on a hyperboloid embedded in 5D Minkowski space: $$ -( x^0)^2+( x^1)^2+( x^2)^2+( x^3)^2+( x^4)^2=\pm \...
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de Sitter space vs de Sitter universe

I have heard of the term de Sitter space. From this post user G. Smith writes, De Sitter spacetime is curved; specifically, it has the same positive scalar curvature at every point. Likewise, when I ...
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Positive and negative curvature de Sitter spacetimes

I'm reading Mukhanov's "Physical foundations of cosmology" and in the section on the de Sitter universe, he examines a perfect fluid with pressure $p$ equal to negative of the energy density ...
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Double Wick Rotation of de Sitter Metric with Closed Slicing

The de Sitter spacetime (with closed spherically symmetric slicing) has the metric $$\text{d}s^2 = -\text{d}t^2 + \alpha^2\cosh(t/\alpha)^2\text{d}\Omega_{d-1}^2$$ where $\text{d}\Omega_{d-1}^2$ is ...
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Negative surface tension of de Sitter event horizon?

Questions – What does a negative surface tension of a de Sitter cosmological event horizon actually mean? Scotch in water, or something else? What does a zero ‘external’ vacuum pressure to the de ...
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Confusion with timelike geodesics in de Sitter space

Without deriving the whole geodesic, I'm thinking I should be able to qualitatively see how the geodesics will curve just by looking at the connection coefficients. Given the static coordinates $$ds^...
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F-theory questions on MSSM vs. SM compatibility and on de Sitter vacua

Having read https://arxiv.org/abs/2112.03947, https://arxiv.org/abs/1903.00009 and https://arxiv.org/abs/1903.00009, I noted the use of MSSM (Minimal Supersymmetric Standard Model) as if equivalent to ...
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Can we glue the Schwarzschild and the de Sitter metrics at their event horizon?

Is there a way to glue the de Sitter metric inside the event horizon of the Schwarzschild metric, without an explicit reference to a particular coordinates system? Using the standard radial ...
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Is the number of possible values of a quantum observable finite, countably infinite or uncountably infinite?

Do we know, or have a theory about, whether the number of possible values any fundamental quantum property can assume upon observation is finite, countably infinite or uncountably infinite?
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Can a massless electric charge particle exist in a de Sitter universe?

Because of the cosmological constant, our universe may reach a de Sitter universe in the far future. If we suppose this, the most basic group of particle physics will be the Sitter, rather than ...
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Holographic Degrees of Freedom

What does it mean when one says "holographic degrees of freedom" in dS space? As Susskind does in his recent papers, the latest here (page 18).
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Why do string theorists seem to ignore cosmology?

Related and sort of a follow-up question to: If string theory is inconsistent with observations, why hasn't it been rejected yet? From the answer to that question, string theorists are aware the ...
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Why are the radius of the observable universe and radius of curvature of dark energy almost the same?

If you take the Einstein equation, $R_{\mu\nu} - \frac12 Rg_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}$ and plug in the estimated vacuum energy of $10^{-9} J/m^3$ for $T_{\mu\mu}$, you get a spatial ...
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Anti de Sitter & de Sitter Spacetime [duplicate]

Can anyone please explain what are the Anti de Sitter and de Sitter spacetime and what is special about them? I am learning general relativity and I stumbled upon them a few times, even on the subject ...
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De Sitter horizon area increase

Black holes increase area when any object falls past the horizon. Note: We define "when" as when the hair from the object falling in becomes undetectable for distant observers. It would also ...
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Is there a smooth, spherically symmetric, static, asymptotically de Sitter spacetime of constant scalar curvature?

...other than de Sitter space itself? Two clarifications: I am not talking about solutions of Einstein's equations, just spacetimes. So, general Lorentzian manifolds. I am not counting, for example,...
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The contravariant derivative of a substitution for the de Sitter metric

Consider the de Sitter metric: $$ds^2 = (1-\frac{r^2}{a^2})dt^2 -(1-\frac{r^2}{a^2})^{-1}dr^2-r^2d\Omega^2$$ I know that we rewrite the metric as $(u,r,\theta \phi)$ using the substitution $$u = t-...
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Timelike geodesics of 2-dimensional de Sitter spacetime

The de Sitter spacetime in two dimensions ($\text{dS}_2$) can be spanned by two coordinates : $\tau$ and $\phi$ (can be viewed as a cylinder). The metric is then defined as follows : $$ds^2=-d\tau^2+\...
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Construction of Carter-Penrose diagram for DeSitter spacetime

The DeSitter spacetime line element in global coordinates is given by $$ds^2 = -dt^2 + \frac{1}{H^2}\cosh^2(Ht)\left(d\chi^2 + \sin^2(\chi)(d\theta^2 + \sin^2(\theta)d\phi^2 \right).$$ The ranges of ...
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Bose-Einstein statistics in de Sitter spacetime

The metric in de Sitter spacetime with $(+,-,-,-)$ as metric signature is, in cartesian coordinates: \begin{equation} ds^2=dt^2-a^2(t)(dx^2+dy^2+dz^2). \end{equation} Where $a(t)=e^{Ht}$. How do I ...
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de Sitter Spacetime: Static patch vs Global coordinates

Two well-known coordinate charts on the dS spacetime are the global coordinates and the static patch coordinates. In the global coordinates, the D-dimensional dS metric takes the following form $$ ds^...
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How to check if some metric has a particular type of geodesics?

For instance, we want to know if cylindrically symmetric de Sitter-type spacetime has an axial geodesic. This is the metric I am interested in $$ds^2= \cos^{\frac{4}{3}}\left(\frac{\sqrt{3 \Lambda}}{2}...
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Interpretation of horizon in de Sitter

Given the de Sitter metric for spacetime $$ds^2 = \left( 1 - \frac{\Lambda}{3}r^2\right) dt^2 - \frac{1}{\left( 1 - \frac{\Lambda}{3}r^2 \right)}dr^2 - r^2d\Omega^2 $$ we understand this is a solution ...
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How does $1/r$ gravity change in de Sitter space?

Classical $1/r$ gravity arises from general relativity when curvature is neglected and speeds are small compared to the speed of light. In de Sitter space with a positive cosmological constant $\...
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Understanding Verlinde: How to get from emergent gravity to MOND

Verlinde ( https://arxiv.org/abs/1611.02269 ) tries to deduce MOND from emergent gravity. Can you help? Emergent or entropic gravity goes back to Jacobson. He starts with the entropy-area connection $...
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de-Sitter space as near-horizon limit of Black Holes

We know that we can obtain $AdS_{2}$ x $S_{2}$ spacetime as the near-horizon geometry of an extremal/ near extremal RN (or Kerr) Black Hole in asymptotically flat spacetime. It is also known that we ...
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Is de Sitter space homogeneous?

Since Minkowski and anti de Sitter are homogeneous Lorentzian manifolds, it is natural to ask if de Sitter is too, but nobody ever discusses this. In Riemannian geometry a globally symmetric complete ...
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Jacobi Identity in de Sitter Superalgebra

In the book "Supergravity" (by D. Freedman and A. Van Proeyen) they talk about why $\mathcal{N}=1$ de-sitter superalgebra is impossible to construct (Section 12.6.1). Basically de-Sitter algebra is a ...
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Casimir operators of de Sitter space

De-Sitter space can be thought of as a 4 dimensional hyperboloid embedded in 5D Minkowski space. Hence, the symmetry group of dS is $SO(1,4)$ whose generators are, $J_{AB}=i\left(X_A\frac{\partial}{\...
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de Sitter vacua in String Theory

I don't quite understand what goes wrong with the de Sitter vacua in string theory. Firstly, how are the vacua calculated (I'm given to understand there is no standard method, so what are the efforts ...
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Does de Sitter space have a preferred frame?

Consider the flat, expanding coordinates for de Sitter space: $$ds^2=-dt^2+e^{2Ht}d\vec{x}^2\quad .$$ This is clearly not invariant under the ordinary Lorentz transformations. Does this mean that if I ...
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Massive particles in de Sitter space

Can massive particles in de Sitter space move faster than light? For the radial coordinate (in static coordinates) I have got the hyperbolic expression $$r(\tau)\propto \sinh\left(\sqrt{\frac{\...
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Supersymmetry in de Sitter space

Is it possible to construct SUSY theories in de Sitter space? I know statement: dS superalgebras cannot be constructed unless one constructs actions with matter coupled with the wrong signs for ...
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Newton's law of gravitation in de Sitter space

Given two masses $M$ and $m$ (with $M\gg m$) in a de Sitter background with cosmological constant $\Lambda>0$ and positive spatial curvature ($k=+1$). What is the corresponding (semiclassical "...
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String Landscape, De Sitter vacua and Broken Supersymmetry

If we assume that the swampland conjectures, etc. regarding de sitter vacuas existence in the string / F-theory landscape turn out to be incorrect (and therefore we can assume the problem is well-...
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How to pick what coordinates transformations to apply in general relativity?

I've been challenged by coordinate transformations lately, as most of you know during solving any problem in GR we have to go through lots of transformations, my question is how we decide the best ...
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AdS/CFT phenomenology and realistic FRW model building

Are there any examples of realistic holography (likely as a de Sitter type Universe: as it approximates FRW / is an FRW solution without baryonic and dark matter). I don’t see why one wouldn’t be ...
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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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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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