Quiescent cosmological singularities

TL;DR

This paper rigorously confirms the Belinskii-Khalatnikov-Lifshitz proposal for the structure of spacetime singularities in certain Einstein solutions, showing the existence of specific asymptotic behaviors near singularities.

Contribution

It provides a rigorous proof of the BKL conjecture for analytic solutions of Einstein equations with scalar fields or stiff fluids, establishing the detailed structure near singularities.

Findings

Existence of solutions with BKL asymptotics

Singularity can be described using Gaussian coordinates

Decoupling of evolution at different spatial points

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.