Spacetime Singularities: Recent Developments

TL;DR

This paper reviews recent progress in understanding spacetime singularities in general relativity, focusing on oscillatory behaviors in both homogeneous and inhomogeneous cosmological models, highlighting mathematical, analytical, and numerical advances.

Contribution

It synthesizes recent rigorous, analytical, and numerical results on oscillatory spacelike singularities, emphasizing hierarchical structures and asymptotic symmetries in diverse cosmological settings.

Findings

Rigorous results for Bianchi types VIII and IX

Analysis of recurring spike formations in inhomogeneous models

Connections between asymptotic behavior and hidden symmetries

Abstract

Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The second deals with generic oscillatory singularities in inhomogeneous cosmologies, especially those with two commuting spacelike Killing vectors. This paper describes recent progress in these two areas: in the spatially homogeneous case focus is on mathematically rigorous results, while analytical and numerical results concerning generic behavior and so-called recurring spike formation are the main topic in the inhomogeneous case. Unifying themes are connections between asymptotic behavior, hierarchical structures, and solution generating techniques, which provide hints for a link between the nature of generic singularities and a hierarchy of hidden asymptotic symmetries.