Quantum Instability of Black Hole Singularity in Three Dimensions

Abstract

We study an internal structure of (2+1)-dimensional black hole with the neutral scalar matter in the spherically symmetric geometry by using a quantum theory of gravity which holds in the both vicinities of the singularity and the apparent horizon. A special attention is paid to the quantum-mechanical behavior of the singularity in the black hole. We solve analytically the Wheeler-DeWitt equation of a minisuperspace model where the ingoing Vaidya metric is used as a simple model representing a dynamical black hole. The wave function obtained in this way leads to interesting physical phenomena such as the quantum instability of singularity and the Hawking radiation. It is also pointed out a similarity between the singularity in (2+1)-dimensional black hole and the inner Cauchy horizon in (3+1)-dimensional Reissner-Nordstrom charged black hole.