Questions tagged [de-sitter-spacetime]

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Emergent Entropic Gravity from Quantum Entanglement in de Sitter Space?

Question: Is there already a theory (formula) available for emergent entropic gravity from Quantum Entanglement in de Sitter space? For detailed background information please refer to a recent ...
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Can the General Relativity Energy Relation of the Static Patch of deSitter Space be Quantized?

I am trying to play around with quantum field theory in de Sitter space. In reading a lecture about General Relativity, I found that, in the static patch of de Sitter space, the conserved quantity of ...
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de Sitter spacetime, spacetime without boundaries and holographic principle

One of the most intriguing aspects of black hole thermodynamics is that of holography or the holographic principle, namely, that the degrees of freedom of a putative theory of quantum gravity is ...
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Conformal flatness of $\rm dS$ spacetime

There exists a flat slicing in the lower triangle area of the Penrose diagram of $\rm dS$ spacetime. To see this point, one introduces the planner coordinate, as defined in eq(13) of Les Houches ...
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Cosmological understanding from Penrose diagram of de Sitter spacetime

The conformal diagram of de Sitter spacetime looks like this I think I understand the causal properties of this diagram. Someone who is static in the south pole can send messages only to the upper ...
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Question about cosmological constant and radius of curvature of the universe

Dimensional analysis suggests that $\Lambda R^2 \sim O(1)$, where $\Lambda$ is the cosmological constant and $R$ is the radius of the universe. $\Lambda$ is measured to be around $10^{-52}$ m$^{-2}$, ...
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Carter Constant with a Cosmological Constant

The Carter constant for the Kerr Newman metric $$ \rm C = p_{\theta}^{2} + \cos^{2}\theta \ \Bigg[ a^2 \ (m^2 - E^2) + \left(\frac{L_z}{\sin\theta} \right)^{2} \Bigg] $$ with (in $[+---]$ signature) $$...
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A question about de Sitter-invariant general relativity

In the case of standard general relativity, all solutions to the gravitational field equations are spacetimes that reduce locally to Minkowski. Einstein’s equation is written as $R^{\mu \nu}-\frac{1}{...
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Is the limit from $d\mathcal{S}_4$ to Minkowski spacetime smooth?

For a static observer, the boundary of observed $dS^4$ spacetime locates on $r=\ell$, $\ell$ is the de Sitter radius which is reversely proportional to spacetime curvature or say cosmological constant ...
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DeSitter cosmological horizon stability?

If the universe keeps expanding at an accelerated rate (given by the cosmological constant) then the universe would approach a DeSitter spacetime where there would be a cosmological horizon that would ...
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Can a black hole in a quasi-de Sitter universe have scalar hair?

Any static and axially symmetric, asymptotically flat black hole spacetime cannot support scalar hair. The universe is not asymptotically flat since it is quasi-de Sitter. Could we find a black hole ...
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Textbooks on the Schwarzschild-de-Sitter Metric

Does anybody know a textbook on the geometry of the Schwarzschild-de-Sitter metric and its maximal extension? It's not in Hawking & Ellis.
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Trying to get a metric like $ds^2 = -e^{2H_0t} dt^2 + dx^2$ from a higher dimensional Minkowski spacetime

Since the 4D de Sitter spacetime can be found by slicing up a 5D Minkowski spacetime: de Sitter space from generalized Minkowski spacetime resulting in a metric like: $ds^2 = - dt^2 + e^{2H_0t} dx^2$ ...
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de Sitter space from generalized Minkowski spacetime

I'm trying to follow this: "The metric on de Sitter space is the metric induced from the ambient Minkowski metric." https://en.wikipedia.org/wiki/De_Sitter_space What I have in mind is ...
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Penrose diagram of de Sitter spacetime: Constant time curve on $r>R$ domain

I have to draw penrose diagram of $dS_4$, with its constant time and space curves. Static patch of $dS_4$: $$ds^2=-(1-(r/R)^2)dt^2+1/(1-(r/R)^2)dr^2+r^2d\Omega_2^2$$ And conformally transformed into ...
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Spatial translational invariance for de Sitter spacetime

Consider de Sitter spacetime in the 'flat slicing' i.e. in the coordinates $$ds^2 = a(\tau)^2\left[-d\tau^2 + dx^2 + dy^2 + dz^2\right],$$ where $x,y,z$ are Cartesian coordinates for space and $\tau$ ...
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How to move from AdS to dS space?

I studied different black holes in different spacetime and I also checked their differences, for example, the difference that exists in dS and AdS spaces. The question that has been created for me is ...
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How to calculate the total entropy of dS black holes?

In several articles where the thermodynamics of dS black holes have been investigated, the entropy part of the model or the total entropy has been analyzed based on the entropy of the black hole ...
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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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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 ...
spacetime's user avatar
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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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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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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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