Quiescent Cosmological Singularities |
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Authors: | Lars Andersson Alan D Rendall |
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Institution: | Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden.?E-mail:larsa@math.kth.se, SE Max–Planck–Institut für Gravitationsphysik, Am Mühlenberg 1, 14424 Golm, Germany.?E-mail: rendall@aei-potsdam.mpg.de, DE
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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.
Received: 17 January 2000 / Accepted: 27 November 2000 |
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