Variational principle for gravity in the extended phase space

TL;DR

This paper develops a variational formalism in extended phase space for gravity, revealing how local inertial invariance constrains torsion and matter coupling, and showing that Einstein-Hilbert dynamics occur on torsion-free surfaces.

Contribution

It introduces a novel variational approach in extended phase space that links torsion, matter fields, and gravitational dynamics under local inertial invariance.

Findings

Torsion couples to matter fields via a 3-form.

Invariance under local inertial frames constrains torsion.

Einstein-Hilbert dynamics occur on torsion-free surfaces.

Abstract

Variational formalism in the extended phase space for fields is applied to gravity. It is shown that the requirement of invariance under arbitrary local inertial frames implies a coupling of torsion to a 3-form of matter fields on the one hand and to a 3-form (related to the Einstein tensor) on the other. Gravitational dynamics is restricted to torsion zero surface in the extended phase space for Einstein-Hilbert action.