The reduced phase space of Palatini-Cartan-Holst theory

TL;DR

This paper characterizes the reduced phase space of Palatini-Cartan-Holst gravity using geometric methods, clarifying its relation to the Einstein-Hilbert formulation of general relativity.

Contribution

It provides a geometric description of the reduced phase space for Palatini-Cartan-Holst theory and compares it with the Einstein-Hilbert approach.

Findings

Explicit description of the reduced phase space

Relation established between Palatini-Cartan-Holst and Einstein-Hilbert formulations

Clarification of gauge symmetries and constraints

Abstract

General relativity in four dimensions can be reformulated as a gauge theory, referred to as Palatini-Cartan-Holst theory. This paper describes its reduced phase space using a geometric method due to Kijowski and Tulczyjew and its relation to that of the Einstein-Hilbert approach.