Re: Singularities
carlip-nospam_at_physics.ucdavis.edu
Date: 02/09/05
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Date: Wed, 9 Feb 2005 18:08:57 +0000 (UTC)
Ramkins <ramkinkar@gmail.com> wrote:
> Cosmological solutions are there that had singularities in their past.
> FRW universes with dust or radiation have a singularity in their past.
> A solution like the closed de Sitter solution has no singularity.
> So a cosmological constant or a vacuum fluid can avoid such a
> singularity.
> Generally, what are the necessary criteria for a past singularity?
I don't think much is known about necessary criteria. Several sets
of *sufficient* criteria are given by the Hawking-Penrose singularity
theorems; generally these involve matter satisfying some positive
energy condition plus a past trapped surface. De Sitter space avoids
a singularity because a cosmological constant, considered as part of
the stress-energy tensor, violates the positive energy requirements.
You can find details in Hawking and Ellis, _The large scale structure
of space-time_, or in chapter 9 of Wald's textbook, _General Relativity_.
(I imagine there are less technical sources as well, but don't know
of any off hand. For FRW spaces, it's easier; there will be a past
singularity if the density rho is positive and the pressure p is
non-negative.)
Steve Carlip
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