Low regularity extensions beyond Cauchy horizons

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