Low regularity extensions beyond Cauchy horizons

TL;DR

This paper investigates the structure of Cauchy horizons in spacetimes with continuous metrics, linking their formation to causal curves or points at infinity, and relates this to cosmic censorship and a PDE formulation.

Contribution

It establishes a new connection between low regularity spacetime metrics and the formation of Cauchy horizons, advancing understanding of cosmic censorship conjectures.

Findings

Cauchy horizons are caused by almost closed causal curves or points at infinity.

The results relate to strong cosmic censorship and Wald's conjecture.

Reformulates Wald's conjecture as a PDE problem regarding horizon locations.

Abstract

We prove that if in a spacetime endowed with a merely continuous metric, a complete partial Cauchy hypersurface has nonempty 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 reformulated as a PDE problem about the location of Cauchyh horizons inside black hole interiors.