Black-hole decay and topological stability in quantum gravity

Abstract

We show that black holes are topologically stable under quantum fluctuations but unstable under quantum emission and absorption of gravitons. The probability of emission behaves as exp[-\ensuremath{\alpha}(${M}_{f}$-${M}_{i}$)], where ${M}_{i}$ and ${M}_{f}$ are the masses associated to the initial and final states, and \ensuremath{\alpha} is a positive constant of the order of 1. As the black hole loses mass it evolves towards a state corresponding to a black hole of very small mass that cannot be distinguished from a pure graviton state.