Mathematical Structure of Tetrad Equations for Vacuum Relativity

TL;DR

This paper analyzes the mathematical structure of tetrad equations in vacuum relativity, demonstrating their well-posedness and deriving associated geometric and Lagrangian forms.

Contribution

It reveals the well-posedness of Buchman and Bardeen's tetrad equations using Cartan characters and introduces a Cartan 4-form and Lagrangian density for the theory.

Findings

Tetrad equations are shown to be well posed.

A Cartan 4-form for the field theory is derived.

An intrinsic Lagrangian density is identified.

Abstract

The tetrad partial differential equations formulated by Buchman and Bardeen for vacuum gravity are shown to be well posed by calculation of the Cartan characters of an associated exterior differential system. Gauge specializations are discussed. A Cartan 4-form is found for this field theory, together with its intrinsic version the Lagrangian density.