Black-hole polarization and cosmic censorship

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 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 redshifted 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 two factors not considered in former gedanken experiments: the effect of the spacetime curvature on the electrostatic self-interaction of the charged system (the black-hole polarization), and the finite size of the charged body.