Spacetime singularities and curvature blow-ups

TL;DR

This paper explores the conditions under which curvature blow-ups occur in spacetime singularities, linking cosmic censorship hypotheses to the behavior of tidal forces and frame-dragging in incomplete geodesics.

Contribution

It demonstrates that under a low regularity form of the strong cosmic censorship hypothesis, curvature blow-ups are inevitable in generic timelike geodesically incomplete spacetimes.

Findings

Curvature blow-ups are linked to cosmic censorship.

Blow-ups occur in tidal force and frame-drag parts of curvature.

Results apply to maximal Cauchy developments.

Abstract

The singularity theorems of Penrose, Hawking, and Geroch predict the existence of incomplete inextendible causal geodesics in a wide range of physically adequate spacetimes modeling the gravitational collapse of stars and the expanding universe. Here, using results on spacetime extensions, it is shown that if a suitable low regular form of the strong cosmic censor hypothesis holds, then parallelly propagated blow-up of either the tidal force or frame-drag part of the curvature must occur in ``generic'' timelike geodesically incomplete maximal Cauchy developments.