Timelike singularities and Hamiltonian cosmological billiards

TL;DR

This paper constructs a broad class of vacuum solutions to Einstein's equations near timelike singularities, challenging existing heuristic models and providing new insights into the nature of such singularities.

Contribution

It introduces a novel Fuchs analysis approach to generate solutions without symmetries and examines the impact of sign changes in Hamiltonian walls on cosmological billiard models.

Findings

Constructed vacuum solutions with controlled asymptotics near timelike singularities.

Identified that sign changes in Hamiltonian walls invalidate previous heuristic models.

Challenged the applicability of cosmological billiards to certain singularity contexts.

Abstract

We construct a large class of vacuum solutions of the Einstein equations without any symmetries and with controlled asymptotics near a timelike singularity. The solutions are obtained by a Fuchs analysis of the equations which evolve the metric in a spacelike direction. We further observe that the changes of signs of some of the terms (walls) in the associated Hamiltonian invalidate the "cosmological billards" heuristic arguments for existence of singularities of mixmaster type in the current context.