# Tag Info

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We are already living in a nearly empty de Sitter space - the cosmological constant already represents 73% of the energy density in the Universe - and the Universe won't experience any qualitative change in the future: the percentage will just approach 100%. However, once the space may be approximated as an empty de Sitter space, all moments of time are ...

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The answer is trivially yes. When large AdS blackholes radiate, the Hawking radiation is 'reflected' at infinity, and you eventually end up with a sort of thermodynamic equilibrium state where the blackhole becomes stable and eternal as it reabsorbs its radiation. The details are a little bit more involved, but suffice it to say nothing like that happens ...

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One may always choose any coordinates on a spacetime manifold or any other manifold, for that matter. That's not only a simple mathematical insight but also a cornerstone of the general theory of relativity. In fact, GR starts with the postulate that all (non-singular etc.) coordinate systems are as good as any other coordinate systems and the basic laws of ...

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Well it just so happens that Mitchell answered this question in a private email, I'm posting the relevant part here for the greater good. The Wick rotation in this case transforms a local patch of dS space into AdS space, or vice versa. Think of the difference between concave and convex, a valley and a hill. Then you should imagine that we have ...

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Dear inflation, the answer is No, one can't define an asymptotic S-matrix in de Sitter space. See e.g. section V.A. in this paper by Bousso: http://arxiv.org/abs/hep-th/0412197 The problem is that the Penrose diagram of a de Sitter space starts and ends with a horizontal line. So at the beginning, the observer is forbidden - by causality - to set up ...

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That's a good question. These issues have an important philosophical core. But science is ultimately not about philosophy. The robust propositions made by science are about calculations and proofs obtained from empirically validated theories. So it is appropriate to view your question as a scientific one. Then there may actually be a pretty good reason, ...

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I find it helpful to visualize de Sitter space-time using Felix Klein's approach to geometry; begin with projective space and pick a polarity that transforms trivially under the congruence group of the geometry. To get 3+1 de Sitter space-time one starts with a 4-d projective space that is modelled as the rays of a 5-d vector space $V_{5}$; a point in de ...

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The motivation for this construction is explained here: He first gives the example of a space of constant positive curvature - the 3-sphere, given by taking a flat Euclidean space of one higher dimension (4) and restricting to the subspace $(x_1, x_2, x_3, x_4)$ s.t. $$x_1^2+x_2^2+x_3^2+x_4^2=a^2$$ for some $a$. The metric on the sphere is just the ...

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Rie. Like your question. I've been stewing on this for 5 yrs now, but have gotten nowhere. Suggestions. For moral support on the CC, see Carlo Rovelli's great paper:http://arxiv.org/abs/1002.3966. For physics(CC only, no dSS) see Beck: http://arxiv.org/abs/0810.0752 The electron & therefore QED must be involved. Dirac's 1935 paper was first to ...

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The entropy is simply $$S = k_B\cdot \ln N$$ where $N$ is the number of macroscopically indistinguishable microstates. If they transform as a representation of a group, then $N$ is the dimension of this representation. The relevant Hilbert space must be a unitary representation of the isometry groups: the isometries have to preserve the sesquilinear norm ...

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Leonard Susskind, the originator of causal patch complimentarity has lately refined it to "horizon complimentarity". According to horizon complimentarity, a horizon is associated with each point on future conformal infinity, which may be built up from a union of null and spacelike segments with future tips and the like at their intersections. For each point ...

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The Bunch-Davies (BD) vacuum is a "pure state" when it comes to all the creation and annihilation operators in the patch where the BD vacuum is relevant. Inside this patch, we can say what operators annihilate the BD state which uniquely specifies it (well, for massive fields, one has the $\alpha$-vacua as generalizations). However, there's also a thermal ...

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