# Tagged Questions

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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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### Geodesics on dS and AdS

I have been reading through the following paper "The dS and AdS Sightseeing Tour" (http://www.bourbaphy.fr/moschella.pdf) but I am not clear about why geodesics appear as hyperbola in the dS case (see ...
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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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### 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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### 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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### 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 ...
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### Does the background spacetime of a black hole affects its thermodynamic properties?

The question is this: will the thermodynamic properties of a black hole (Hawking radiation spectra and temperature, entropy, area, etc.) depend if the black hole sits in a DeSitter or an Anti-De-...
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### Visualization of de Sitter spaces

When I was reading about de Sitter it said that the we looked in 5-dimensional Minkowski metric and that we had immersed in it a hyperboloid, and with some coordinate transformation we get some metric ...
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### How to calculate temperature and entropy on Schwarzschild-de Sitter space

The cosmological event horizon found in a de Sitter universe has some interesting similarities to that of a black hole. For example, since we can find a temperature at the horizon, we are able to use ...
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### How should one interpret the de Sitter slicings?

When 'constructing' the usual de Sitter space in $\mathcal{M^5}$ by invoking the contraint $-X^{2}_{0} +X^{2}_{1} +X^{2}_{2} +X^{2}_{3} + X^{2}_{4} = \alpha^2$ we quickly see that we end up with a ...
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### How do representations of an isometry group correspond to degrees of freedom/entropy in a system?

To put the question into context: I am currently writing my bachelors thesis on de Sitter space, specifically, $dS_4$. I am trying to show that while the horizon entropy is finite, the isometry group \$...
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### How is causal patch complementarity compatible with behavior during inflation?

Causal patch complementarity is the conjecture that in de Sitter space with a positive cosmological constant, the states within the causal patch are sufficient to fully describe the universe with the ...
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### Partition Functions in (A)dS/CFT

I'm trying to understand some aspects of dS/CFT, and I'm running into a little trouble. Any help would be much appreciated. In arXix:1104.2621, Harlow and Stanford showed that the late-time Hartle-...
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### AdS to dS uplifting and its opposite

So as I understand it, localized structures in AdS can wick rotated to dS, the boundary has to be complixified as can be seen here. Also, uplifting is another technique that can be used to move from ...
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### Please justify invoking logical positivism to causal patches and black hole interiors in quantum gravity! [closed]

Logical positivism is often invoked to explain why external observers can't talk about black hole interiors, or why we can't talk about what happens outside our causal patch in inflationary models. ...
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### Does de Sitter space admit an asymptotic S-matrix?

From the Penrose diagram of de Sitter space, we see it has a future and past conformal boundary, and they are both spacelike. So, does de Sitter space admit an asymptotic S-matrix? Sure, in the usual ...