On rigidity of spacetimes with a compact Cauchy horizon

TL;DR

This paper proves that smooth spacetimes with a non-degenerate compact Cauchy horizon ruled by closed null geodesics necessarily admit a smooth Killing vector field nearby, supporting Penrose's strong cosmic censorship hypothesis.

Contribution

It establishes the existence of a smooth Killing vector field near such horizons, demonstrating a rigidity property of these spacetimes.

Findings

Existence of a smooth Killing vector field near the horizon

Supports Penrose's strong cosmic censorship hypothesis

Shows rigidity of spacetimes with compact Cauchy horizons

Abstract

Smooth spacetimes with a compact Cauchy horizon ruled by closed null geodesics are considered. The compact Cauchy horizon is assumed to be non-degenerate. Then, supporting the validity of Penrose's strong cosmic censor hypothesis, the existence of a smooth Killing vector field in a neighbourhood of the horizon on the Cauchy development side is shown.