A New Class of Asymptotically Non-Chaotic Vacuum Singularities

TL;DR

This paper constructs a new class of four-dimensional vacuum spacetimes with spacelike singularities that exhibit non-chaotic behavior without relying on symmetry assumptions, expanding understanding of singularity dynamics.

Contribution

It introduces a novel method to construct non-chaotic vacuum singularities without symmetry constraints, using Iwasawa variables and asymptotic conditions.

Findings

Constructed solutions contain five free functions of space.

Solutions exhibit non-chaotic behavior near singularities.

Compared new solutions with previous models and analyzed asymptotics.

Abstract

The BKL conjecture, stated in the 60s and early 70s by Belinski, Khalatnikov and Lifshitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some of them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.