Fluid Entropy as Time-Variable in Canonical Quantum Gravity

TL;DR

This paper applies the Brown-Kuchar mechanism to canonical quantum gravity coupled with a perfect fluid, deriving a physical Hamiltonian that incorporates fluid entropy as a time variable.

Contribution

It introduces a novel approach to defining time evolution in quantum gravity by using fluid entropy within the canonical formalism.

Findings

Derived a physical Hamiltonian as a functional of gravitational variables and entropy.

Reconstructed the notion of time evolution in quantum gravity with fluid coupling.

Demonstrated the applicability of the Brown-Kuchar mechanism in this context.

Abstract

The Brown-Kucha\v{r} 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.