Trapped Surface as a Cosmic Censor

Abstract

We formulate a local geometric criterion for weak cosmic censorship in black hole overcharging and overspinning thought experiments. Under the null convergence and generic conditions, matter injection turns a horizon cross section into a closed trapped surface. Any final spacetime unable to accommodate this surface is ruled out. This trapped surface criterion excludes superextremal Reissner-Nordström, Reissner-Nordström-de Sitter, and Kerr-Newman final states, as well as Weyl-class naked singularities. Our criterion does not rely on asymptotic charges or on an extremal condition characterizing naked singularities.

9 pages, 1 figure