Causal Propagation of Constraints in General Relativity

TL;DR

This paper proves that the constraint functions in general relativity are propagated by a hyperbolic system aligned with the light cone, based on Bianchi identities, without requiring analyticity.

Contribution

It establishes that constraint propagation in general relativity follows a hyperbolic system derived from Bianchi identities, without the need for analyticity assumptions.

Findings

Constraint functions are propagated by a hyperbolic system.

The characteristic cone of the system is the light cone.

Analyticity is not required for the proof.

Abstract

In this paper, I demonstrate that the constraint functions are propagated by a first order symmetric (or symmetrizable) hyperbolic system whose characteristic cone is the light cone. This result follows from the twice-contracted Bianchi identities. Analyticity is not required.