The Husain-Kuchar Model: Time Variables and Non-degenerate Metrics

TL;DR

This paper introduces a new action principle for the Husain-Kuchar model, featuring a scalar time variable and a non-degenerate metric, facilitating the definition of geometric observables and matter coupling.

Contribution

It presents a novel action with a scalar time variable and non-degenerate metric, enhancing the model's physical interpretability and coupling capabilities.

Findings

Presence of a scalar time variable enabling geometric observables

Emergence of a natural non-degenerate four-metric

Potential for coupling ordinary matter

Abstract

We study the Husain-Kuchar model by introducing a new action principle similar to the self-dual action used in the Ashtekar variables approach to Quantum Gravity. This new action has several interesting features; among them, the presence of a scalar time variable that allows the definition of geometric observables without adding new degrees of freedom, the appearance of a natural non-degenerate four-metric and the possibility of coupling ordinary matter.