Quiescent Cosmological Singularities

By Lars-Erik Andersson, A. Rendall. 2000

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Abstract: The most detailed existing proposal for the structure of spacetime singularities originates in the work of Belinskii, Khalatnikov and Lifshitz. We show rigorously the correctness of this proposal in the case of analytic solutions of the Einstein equations coupled to a scalar field or stiff fluid. More specifically, we prove the existence of a family of spacetimes depending on the same number of free functions as the general solution which have the asymptotics suggested by the Belinskii–Khalatnikov–Lifshitz proposal near their singularities. In these spacetimes a neighbourhood of the singularity can be covered by a Gaussian coordinate system in which the singularity is simultaneous and the evolution at different spatial points decouples.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/07b12398ea20dbaae9eabb05ca58364f996c08e1

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Citations in the corpus

Loop quantum cosmology: a status report (2011, background): “[12] L.”
The Bianchi IX Attractor (2000, methodology): “e latter statement will be made precise below. If the matter model is a stiﬀ ﬂuid the matter will be important, and in that case we prove that the behaviour is quiescent. This should be compared with [2] concerning the structure of singularities of analytic solutions to Einstein’s equations coupled ”
Cosmological Billiards (2002, background): “• The billiard of gravity coupled to a dilaton always has infinite volume, hence exhibits Kasner-like behaviour [2, 5, 29].”
TOPICAL REVIEW: Cosmological billiards (2002, background): “The coupling to matter fields does not change the picture, except if one includes a massless scalar field (equivalent to a perfect fluid with “stiff” equation of state p = ρ), in which case the chaotic evolution is replaced by a monotonic power law evolution of the scale factors [5, 2 ], which mimi”
Holographic description of AdS cosmologies (2005, background): “This relation will have to include the fact that our truncated theory of four dimensional gravity coupled to a scalar does not exhibit this chaotic behavior [38, 39].”
Loop quantum cosmology of Bianchi I models (2009, result): “By now considerable evidence has accumulated in favor of this conjecture [27–31].”