Diffeomorphism Invariance of Geometric Descriptions of Palatini and Ashtekar Gravity

TL;DR

This paper proves that the presymplectic forms in Palatini and Ashtekar gravity vanish along gauge orbits, confirming their invariance under diffeomorphisms, which is crucial for their consistency as gravitational theories.

Contribution

It provides an explicit proof of diffeomorphism invariance for Palatini and Ashtekar formulations by analyzing their presymplectic structures.

Findings

Presymplectic forms are zero along gauge orbits.

Diffeomorphism invariance is explicitly confirmed.

Ensures consistency of geometric gravity formulations.

Abstract

In this paper, we explicitly prove the presymplectic forms of the Palatini and Ashtekar gravity to be zero along gauge orbits of the Lorentz and diffeomorphism groups, which ensures the diffeomorphism invariance of these theories.