Polynomial form of the Hilbert-Einstein action

TL;DR

This paper reformulates the Hilbert-Einstein action in general relativity to a polynomial form by extending the configuration space to include the metric determinant as an independent variable.

Contribution

It introduces a novel polynomial formulation of the Hilbert-Einstein action by extending the configuration space with the metric determinant.

Findings

The action becomes polynomial in the extended configuration space.

The reformulation simplifies certain calculations in general relativity.

Potential applications in quantum gravity and computational methods.

Abstract

Configuration space of general relativity is extended by inclusion of the determinant of the metric as a new independent variable. As the consequence the Hilbert-Einstein action takes a polynomial form.