Parametrizing fluids in canonical quantum gravity

TL;DR

This paper explores fluid parametrizations in canonical quantum gravity, focusing on the Brown-Kuchar mechanism to address the problem of time by coupling matter to gravity, with specific models yielding singularity-free or evolutionary solutions.

Contribution

It analyzes scalar and Schutz fluid models within the Brown-Kuchar framework, revealing how entropy and matter coupling influence the physical Hamiltonian and the problem of time.

Findings

Schutz's model provides a singularity-free solution with entropy defining the Hamiltonian.

In the co-moving frame, the time variable relates to the logarithm of entropy.

A generalized scalar fluid model offers an evolutionary picture only in a singular case.

Abstract

The problem of time is an unsolved issue of canonical General Relativity. A possible solution is the Brown-Kuchar mechanism which couples matter to the gravitational field and recovers a physical, i.e. non vanishing, observable Hamiltonian functional by manipulating the set of constraints. Two cases are analyzed. A generalized scalar fluid model provides an evolutionary picture, but only in a singular case. The Schutz' model provides an interesting singularity free result: the entropy per baryon enters the definition of the physical Hamiltonian. Moreover in the co-moving frame one is able to identify the time variable tau with the logarithm of entropy.