Inhomogeneous charged black hole solutions in asymptotically anti-de Sitter spacetime

Abstract

We investigate static inhomogeneous charged planar black hole solutions of the Einstein-Maxwell system in an asymptotically anti-de Sitter spacetime. Within the framework of linear perturbations, the solutions are numerically and analytically constructed from the Reissner-Nordstr\"{o}m-AdS black hole solution. The perturbation analysis predicts that the Cauchy horizon always disappears for any wavelength perturbation, supporting the strong cosmic censorship conjecture. For extremal black holes, we analytically show that an observer freely falling into the black hole feels infinite tidal force at the horizon for any long wavelength perturbation, even though the Kretschmann scalar curvature invariant remains small.