Strong cosmic censorship and Misner spacetime

TL;DR

This paper investigates the stability of the Cauchy horizon in Misner spacetime, showing that small perturbations lead to curvature singularities, thus supporting strong cosmic censorship.

Contribution

It proves that in various gravity theories, perturbations cause curvature singularities at the Cauchy horizon, reinforcing the strong cosmic censorship conjecture.

Findings

Perturbations induce curvature singularities at the Cauchy horizon.

Neighboring solutions in different theories end at the horizon with singularities.

Misner spacetime's extension beyond the horizon is unstable under perturbations.

Abstract

Misner spacetime is among the simplest solutions of Einstein's equation that exhibits a Cauchy horizon with a smooth extension beyond it. Besides violating strong cosmic censorship, this extension contains closed timelike curves. We analyze the stability of the Cauchy horizon, and prove that neighboring spacetimes in one parameter families of solutions through Misner's in pure gravity, gravity coupled to a scalar field, or Einstein-Maxwell theory, end at the Cauchy horizon developing a curvature singularity.