The gauge group in the real triad formulation of general relativity

TL;DR

This paper explicitly constructs generators for gauge symmetries in a vacuum gravity model using a Palatini formulation with specific dynamical variables, clarifying the structure of diffeomorphisms and triad rotations.

Contribution

It provides explicit forms of generators for projectable diffeomorphisms and triad rotations in a Palatini-based gravity model, highlighting the role of gauge variables and the necessity of combined transformations.

Findings

Time-foliation-altering diffeomorphisms require accompanying triad rotations.

Generators act on the full phase space including all gauge variables.

Explicit construction clarifies gauge symmetry structure in the model.

Abstract

We construct explicitly generators of projectable four-dimensional diffeomorphisms and triad rotation gauge symmetries in a model of vacuum gravity where the fundamental dynamical variables in a Palatini formulation are taken to be a lapse, shift, densitized triad, extrinsic curvature, and the time-like components of the Ricci rotation coefficient. Time-foliation-altering diffeomorphisms are not by themselves projectable under the Legendre transformations. They must be accompanied by a metric- and triad-dependent triad rotation. The phase space on which these generators act includes all of the gauge variables of the model.