Integrability in tetrad formalisms and conservation in cosmology

TL;DR

This paper reviews integrability conditions in tetrad formalisms, clarifies their relation to Bianchi equations, and demonstrates how conservation of constraints in cosmology follows from these equations.

Contribution

It clarifies the role of integrability conditions in tetrad formalisms and connects recent conservation results in cosmology to fundamental Bianchi equations.

Findings

Integrability conditions are linked to Bianchi equations.

Additional constraints influence integrability.

Conservation of constraints follows from Bianchi equations.

Abstract

Integrability in general tetrad formalisms is reviewed, following and clarifying work of Papapetrou and Edgar. The integrability conditions are (combinations of) the Bianchi equations and their consequences. The introduction of additional constraints is considered. Recent results on the conservation of constraints in the 1+3 covariant formulation of cosmology are shown to follow from the Bianchi equations