Recent developments concerning generic spacelike singularities

TL;DR

This review summarizes recent advances in understanding generic spacelike singularities in vacuum and matter-influenced spacetimes, highlighting oscillatory behaviors, hierarchical structures, and potential paradigm shifts in their physical interpretation.

Contribution

It connects recent developments in oscillatory singularities, heteroclinic chains, and spike chains within the conformally Hubble-normalized framework, offering new insights into their underlying structures.

Findings

Oscillatory singularities are characterized by complex hierarchical structures.

Connections between asymptotic behavior and heteroclinic chains are established.

Recent progress suggests a possible paradigm shift in understanding the physical role of singularities.

Abstract

This is a review of recent progress concerning generic spacelike singularities in general relativity. For brevity the main focus is on singularities in vacuum spacetimes, although the connection with, and the role of, matter for generic singularity formation is also commented on. The paper describes recent developments in two areas and show how these are connected within the context of the conformally Hubble-normalized state space approach. The first area is oscillatory singularities in spatially homogeneous cosmology and the connection between asymptotic behaviour and heteroclinic chains. The second area concerns oscillatory singularities in inhomogeneous models, especially spike chains and recurring spikes. The review also outlines some underlying reasons for why the structures that are the foundation for generic oscillatory behaviour exists at all, which entails discussing how underlying physical principles and applications of solution generating techniques yield hierarchical structures and connections between them. Finally, it is pointed out that recent progress concerning generic singularities motivates some speculations that suggest that a paradigm shift concerning their physical role, and what mathematical issues to address, might be in order.