De Broglie-Bohm interpretation for analytic solutions of the Wheeler-DeWitt equation in spherically symmetric space-time

摘要

We discuss the implications of a wave function for quantum gravity that involves nothing but 3-dimensional geometries as arguments and is invariant under general coordinate transformations. We derive an analytic wave function from the Wheeler-DeWitt equation for spherically symmetric space-time with the coordinate system arbitrary. The de Broglie-Bohm interpretation of quantum mechanics is applied to the wave function. In this interpretation, deterministic dynamics can arise from a wave function in fully quantum regions as well as in semiclassical regions. By introducing a coordinate system, we obtain a cosmological black hole picture in compensation for the loss of general covariance. [References: 36]