Stability of the black hole horizon and the Landau ghost

The stability of the black hole horizon is demanded by both cosmic censorship and the generalized second law of thermodynamics. We test the consistency of these principles by attempting to exceed the black hole extremality condition in various processes in which a U(1) charge is added to a nearly extreme Reissner-Nordström black hole charged with a different type of U(1) charge. For an infalling spherical charged shell the attempt is foiled by the self-Coulomb repulsion of the shell. For an infalling classical charge it fails because the required classical charge radius exceeds the size of the black hole. For a quantum charge the horizon is saved because, in order to aviod the Landau ghost, the effective coupling constant cannot be large enough to accomplish the removal of the horizon.