Kasner-like regions near crushing singularities

TL;DR

This paper investigates vacuum spacetimes with crushing singularities, establishing a connection between Kasner-like regions and the asymptotic behavior of spatial volume densities under certain curvature bounds.

Contribution

It introduces a relation between Kasner-like regions and volume density asymptotics in vacuum spacetimes with singularities, under scale-invariant curvature bounds.

Findings

Kasner-like regions are characterized by specific asymptotics of volume densities.

Existence of Kasner-like regions depends on curvature bounds.

Results provide insight into the structure of singularities in vacuum spacetimes.

Abstract

We consider vacuum spacetimes with a crushing singularity. Under some scale-invariant curvature bounds, we relate the existence of Kasner-like regions to the asymptotics of spatial volume densities.