A new way to solve Wheeler-DeWitt equation including black hole universe

TL;DR

This paper proposes a novel method to solve the Wheeler-DeWitt equation by expanding the state space to include spacetime metrics, enabling solutions to problems like black hole quantization in quantum gravity.

Contribution

The paper introduces a new approach that enlarges the state functional support to include spacetime metrics, facilitating solutions to longstanding issues in quantum gravity.

Findings

Successfully solved the Wheeler-DeWitt equation with the new method.

Enabled quantization of black holes within the quantum gravity framework.

Provided a pathway to incorporate spacetime metrics in quantum state functionals.

Abstract

One of the unsolved issues in the quantum gravity comes from the Wheeler-DeWitt equation, which is second order functional derivative equation. In this paper, we introduce a new method to solve the Wheeler-DeWitt equation. Usually one treats the state functional of the space of 3-dimensional metrics, which do not contain timelike metrics. However we can expand this state to the state which has support on the space of spacetime metrics with using additional constraint which requires the recovery of 4-dimensional quantum gravity. Enlarging the support of the state functional of the spacetime metrics, we can simply solve the usual Wheeler-DeWitt equation with the additional constraint. Using this method we can solve some unsolved problems, such as the quantization of the black hole.