Quantum Gravity and Black Hole

Abstract

The quantum theory of the spherically symmetric gravity in 3+1 dimensions is investigated. The functional measures are explicitly evaluated and the physical state conditions are derived by using the technique developed in two dimensional quantum gravity. Then the new features which are not seen in ADM formalism come out. If $κ_s > 0 $, where $κ_s =(N-27)/12π$ and $N$ is the number of matter fields, a singularity appears, while for $κ_s <0$ the singularity disappears. The quantum dynamics of black hole seems to be changed by the sign of $κ_s $. (Talk given by K.H. at Workshop on General Relativity and Gravity, Waseda, Tokyo, Japan, 18-20 Jan 1993.)