Low regularity extensions beyond Cauchy horizons

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.

Automated summary

We prove that if a complete partial Cauchy hypersurface in a C(0) spacetime has a non-empty Cauchy horizon, the horizon is caused by almost closed causal curves behind it or by the influence of points at infinity. This result is connected to the concepts of strong cosmic censorship and Wald's conjecture, which can be formulated as a partial differential equation problem regarding the positioning of Cauchy horizons inside black hole interiors.