Black-Hole Polarization and Cosmic Censorship

Abstract

The destruction of the black-hole event horizon is ruled out by both cosmic censorship and the generalized second law of thermodynamics. We test the consistency of this prediction in a (more) `dangerous' version of the gedanken experiment suggested by Bekenstein and Rosenzweig. A U(1)-charged particle is lowered {\it slowly} into a near extremal black hole which is not endowed with a U(1) gauge field. The energy delivered to the black hole can be {\it red-shifted} by letting the assimilation point approach the black-hole horizon. At first sight, therefore, the particle is not hindered from entering the black hole and removing its horizon. However, we show that this dangerous situation is excluded by a combination of {\it two} factors not considered in former gedanken experiments: the effect of the spacetime curvature on the electrostatic {\it self-interaction} of the charged system (the black-hole polarization), and the {\it finite} size of the charged body.