Stability of the Cauchy horizon in anti–de Sitter spacetime

Abstract

A previously developed Cauchy horizon stability conjecture is used to investigate the stability of the Cauchy horizon in the covering space of anti--de Sitter spacetime when infalling and outgoing null dust is introduced. With infalling null dust, the Cauchy horizon is found to be stable, except for the single point r=0 to which the dust collapses. An exact solution of the field equations is presented containing infalling null dust, which reduces to anti--de Sitter spacetime when the dust is removed and which has a nonsingular Cauchy horizon except for a shell-focusing singularity at r=0. The conjecture predicts a nonscalar curvature singularity at r=0, but in fact the shell-focusing singularity is a scalar curvature singularity. When both infalling and outgoing null dust test fields are introduced, the Cauchy horizon is predicted to be stable except for a scalar curvature singularity at r=0.