de Broglie-Bohm Interpretatin for Analytic Solutions of The Wheeler-DeWitt Equation in Spherically Symmetric Space-time

TL;DR

This paper derives an analytic wave function for spherically symmetric quantum gravity using the Wheeler-DeWitt equation and applies the de Broglie-Bohm interpretation to extract deterministic dynamics and a cosmological black hole picture.

Contribution

It introduces a method to obtain analytic solutions for the Wheeler-DeWitt equation in spherically symmetric space-times and applies the de Broglie-Bohm interpretation to interpret quantum gravity.

Findings

Analytic wave function derived for spherically symmetric quantum gravity.

Demonstrates how de Broglie-Bohm interpretation yields deterministic dynamics.

Provides a cosmological black hole picture by breaking general covariance.

Abstract

We discuss the implications of a wave function for quantum gravity, which 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 be yielded from a wave function in fully quantum regions as well as in semiclassical ones. By introducing a coordinate system additionally, we obtain a cosmological black hole picture in compensation for the loss of general covariance. Our analysis shows that the de Broglie-Bohm interpretation gives quantum gravity an appropriate prescription to introduce coordinate systems naturally and extract information from a wave function as a result of breaking general covariance.