Black holes to white holes II: quasi-classical scenarios for white hole evolution

Abstract: This paper considers a wider range of "quasi-classical" models for the non-singular transition from an evaporating black hole to a white hole and the evolution of the white hole than were considered in Paper I. The quantum evolution of the geometry outside a collapsing shell is described by a smoothly evolving spherically symmetric effective metric, with a transition from trapped surfaces in the black hole to anti-trapped surfaces in the white hole at a spacelike hypersurface on which the circumferential radius has a minimum Planck-scale value. Rather than focusing on a specific model for the effective metric and the corresponding effective stress-energy tensor, I consider the general properties of such a transition and the end of the black hole following from the assumption of a smooth geometry. Alternative scenarios for the evolution of the white hole, which avoid the prolonged emission of negative energy from the white hole of the Paper I scenario, are explored. If such a transition, suggested by Loop Quantum Gravity, can be firmly established, the conventional holographic interpretation of the fine-grained entropy of a black hole must be abandoned. It would also be a counter-example to the generalized second law and quantum singularity theorems.