Quantization of the metric diagonal spacetime with Gaussian normal coordinates

TL;DR

This paper simplifies the Wheeler-DeWitt equation for diagonal, Gaussian normal coordinate spacetimes, solving it for universes including Bianchi I and black hole models, advancing quantum cosmology understanding.

Contribution

It introduces a coordinate transformation that simplifies the Wheeler-DeWitt equation for specific diagonal spacetimes, enabling exact solutions for certain universe models.

Findings

Solved Wheeler-DeWitt equation for Bianchi I and black hole universes.

Demonstrated the utility of Gaussian normal coordinates in quantum cosmology.

Provided analytical solutions for simplified quantum gravitational models.

Abstract

In the analysis of the Wheeler-DeWitt equation, we have simplified the Hamiltonian constraint of the Wheeler-DeWitt equation using the coordinate transformation. The coordinate is choose such that metric becomes diagonal and as Gaussian normal coordinate. Or we treat small universe so that the metric become diagonal and universe is covered by Gaussian normal coordinates. We have solved the Wheeler-DeWitt equation of such universes. Such that universe contains Biancki I type universe or the black hole universe.