Testing a stability conjecture for Cauchy horizons

Abstract

A stability conjecture previously developed to investigate quasiregular and nonscalar curvature singularities is extended here to cover the stability of Cauchy horizons. In particular, the Reissner-Nordström spacetime of charged, nonrotating black holes is considered. The conjecture predicts that the addition of infalling null dust with a power-law tail will produce a nonscalar curvature singularity at the Cauchy horizon. This prediction is verified using a Reissner-Nordström-Vaidya spacetime studied by Hiscock. The conjecture also predicts that a combination of infalling and outgoing null dust will produce a scalar curvature singularity at the Cauchy horizon. This prediction is verified using the mass inflation results of Poisson and Israel. Finally, the conjecture predicts that the addition of infalling scalar or electromagnetic waves will produce a scalar curvature singularity at the Cauchy horizon.