NEW RESULTS IN BLACK-HOLE PHYSICS

Brief statements are given on recent results in the following areas: 1 ) The derivation of a variational (maximum) principle for black hole e ntropy, and an outline of the physically reasonable properties of the related solution for the density of states in the microcanonical equil ibrium ensemble (with Jeffrey Melmed, University of Maine). 2) Analysi s of topological contributions to black hole entropy in Lovelock gravi ty, and the corresponding thermodynamic identity (with Jonathan Z. Sim on, University of Maryland). 3) Stability analysis for a shell of matt er surrounding a black hole in microcanonical (thermal) equilibrium (w ith Gerald Horwitz, Hebrew University, Jerusalem) - results from this work can be compared with an earlier analysis of the purely mechanical stability of the shell, and with known properties of both the dynamic al and thermal stability for the black hole without a shell. 4) The st udy of a simple 'singularity'-free model of gravitational collapse, an d an examination of the relationship between the ensuing preservation of quantum coherence and the usual perception that mixed states should be associated with the late time emission of Hawking radiation from a classically formed black hole (with Gerard 't Hooft and Chris Stephen s, University of Utrecht).