Causal propagation of constraints in bimetric relativity in standard 3+1 form

TL;DR

This paper analyzes how constraints propagate in ghost-free bimetric relativity within the 3+1 formalism, demonstrating that their evolution is well-posed and stable, governed by a hyperbolic system aligned with the null cones of both metrics.

Contribution

It establishes that the constraint evolution equations in bimetric relativity form a well-posed hyperbolic system with characteristic cones matching the null cones of the two metrics.

Findings

Constraints evolve according to a symmetric hyperbolic system

Constraint propagation is stable and well-posed

Characteristic cones are the null cones of the two metrics

Abstract

The goal of this work was to investigate the propagation of the constraints in the ghost-free bimetric theory where the evolution equations are in standard 3+1 form. It is established that the constraints evolve according to a first-order symmetric hyperbolic system whose characteristic cone consists of the null cones of the two metrics. Consequently, the constraint evolution equations are well-posed, and the constraints stably propagate.