Definition of a time variable with Entropy of a perfect fluid in Canonical Quantum Gravity

TL;DR

This paper applies the Brown-Kuchar mechanism within canonical quantum gravity to define a time evolution operator involving gravitational variables and entropy, advancing the understanding of time in quantum gravity with perfect fluids.

Contribution

It introduces a novel approach to defining a physical Hamiltonian in canonical quantum gravity coupled with a perfect fluid using the Schutz model.

Findings

Recovered a time evolution operator as a functional of gravitational variables and entropy.

Established a connection between entropy and the evolution of gravitational systems.

Provided a framework for incorporating perfect fluids into quantum gravity models.

Abstract

The Brown-Kuchar mechanism is applied in the case of General Relativity coupled with the Schutz model for a perfect fluid. Using the canonical formalism and manipulating the set of modified constraints one is able to recover the definition of a time evolution operator, i.e. a physical Hamiltonian, expressed as a functional of gravitational variables and the entropy.