NAKED AND THUNDERBOLT SINGULARITIES IN BLACK-HOLE EVAPORATION

If an evaporating black hole does not settle down to a non-radiating remnant, a description by a semi-classical Lorentz metric must contain either a naked singularity or what we call a thunderbolt, a singularity that spreads out to infinity on a space-like or null path. We investigate this question in the context of various two-dimensional models that have been proposed. We find that if the semi-classical equations have an extra symmetry that make them solvable in closed form, they seem to predict naked singularities but numerical calculations indicate that more general semi-classical equations, such as the original CGHS ones give rise to thunderbolts. We therefore expect that the semi-classical approximation in four dimensions will lead to thunderbolts. We interpret the prediction of thunderbolts as indicating that the semi-classical approximation breaks down at the end point of black hole evaporation, and we would expect that a full quantum treatment would replace the thunderbolt with a burst of high-energy particles. The energy in such a burst would be too small to account for the observed gamma ray bursts.