Strong Cosmic Censorship and Causality Violation

TL;DR

This paper examines the stability of Cauchy horizons in compact vacuum universes with causality violations, showing that such violations lead to curvature singularities and supporting the strong cosmic censorship conjecture.

Contribution

It demonstrates that causality violation in compact vacuum spacetimes results in curvature singularities, reinforcing the validity of strong cosmic censorship in these scenarios.

Findings

Causality violation boundary segments become curvature singularities.

Strong cosmic censorship holds in spatially compact vacuum spacetimes.

Causality violation cannot occur in a compact universe.

Abstract

We investigate the instability of the Cauchy horizon caused by causality violation in the compact vacuum universe with the topology $B\times {\bf S}^{1}\times {\bf R}$, which Moncrief and Isenberg considered. We show that if the occurrence of curvature singularities are restricted to the boundary of causality violating region, the whole segments of the boundary become curvature singularities. This implies that the strong cosmic censorship holds in the spatially compact vacuum space-time in the case of the causality violation. This also suggests that causality violation cannot occur for a compact universe.