Strength of the null singularity inside black holes

Abstract

We study analytically the Cauchy horizon singularity inside spherically symmetric charged black holes, coupled to a spherical, self-gravitating, minimally coupled, massless scalar field. We show that all causal geodesics terminate at the Cauchy horizon at a null singularity, which is weak according to the Tipler classification. The singularity is also deformationally weak in the sense of Ori. Our results are valid at arbitrary points along the null singularity, in particular at late retarded times, when nonlinear effects are crucial.