Quantization of static inhomogeneous spacetime

TL;DR

This paper presents a method to quantize certain inhomogeneous spacetime models by solving the Wheeler-DeWitt equation and applying static restrictions, simplifying the Hamiltonian constraint in quantum gravity.

Contribution

It introduces a novel approach to quantize inhomogeneous spacetimes using static restrictions and the up-to-down method, enabling simplification of the Hamiltonian constraint.

Findings

Successfully quantized specific inhomogeneous models

Derived static restrictions that commute with the Hamiltonian constraint in mini-superspace models

Simplified the local Hamiltonian constraint in quantum gravity

Abstract

In this paper we can solve a Wheeler-DeWitt equation of the some inhomogeneous spacetime models as a local solution. From the previous study of up-to-down method we derived the static restriction relating the problem of the time. Although static restriction does not commute with the general Hamiltonian constraint, the Hamiltonian constraint of some mini-superspace models commute with static restriction. We can quantize such inhomogeneous models. With obtained result we can success to simplify the general local Hamiltonian constraint.