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.
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Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. Author information Authors and AffiliationsDepartment of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden.¶E-mail:larsa@math.kth.se, , , , , , SE
Lars Andersson
Max–Planck–Institut für Gravitationsphysik, Am Mühlenberg 1, 14424 Golm, Germany.¶E-mail: rendall@aei-potsdam.mpg.de, , , , , , DE
Alan D. Rendall
Received: 17 January 2000 / Accepted: 27 November 2000
About this article Cite this articleAndersson, L., Rendall, A. Quiescent Cosmological Singularities. Commun. Math. Phys. 218, 479–511 (2001). https://doi.org/10.1007/s002200100406
Issue Date: May 2001
DOI: https://doi.org/10.1007/s002200100406
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