Low regularity extensions beyond Cauchy horizons

M Lesourd,E Minguzzi

doi:10.1088/1361-6382/ac5009

Abstract

We prove that if in a C 0 spacetime a complete partial Cauchy hypersurface has a non-empty Cauchy horizon, then the horizon is caused by the presence of almost closed causal curves behind it or by the influence of points at infinity. This statement is related to strong cosmic censorship and a conjecture of Wald. In this light, Wald’s conjecture can be formulated as a PDE problem about the location of Cauchy horizons inside black hole interiors.

Highlights

Penrose introduced strong cosmic censorship in the seminal paper [26]
In the context of Lorentzian geometry, they formulated a conjecture which they deemed to be in the spirit of strong cosmic censorship
Theorem 2.2. (Cauchy horizons are generated by lightlike geodesics) Let (M, g) be a C0 spacetime and let S be a closed and acausal hypersurface

Summary

Introduction

Penrose introduced strong cosmic censorship in the seminal paper [26]. In an elegant article appearing in the same volume, Geroch and Horowitz [12] elaborated on the differences between the strong and weak formulations of cosmic censorship, and sketched possible approaches one could take to prove such statements. If the maximal Cauchy development of this initial data is extendible, for each p ∈ H+(S) in any extension, either strong causality is violated at p or J−(p) ∩ S is non-compact.1

Results

Conclusion