Low regularity extensions beyond Cauchy horizons

We prove that if in a C0 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.