Initial value constraints with tensor matter

TL;DR

This paper derives a universal form for initial value constraints in covariant metric gravity theories with tensor matter fields, accounting for higher derivatives and applying it to Einstein-aether theory.

Contribution

It introduces a generalized Bianchi identity to derive initial value constraints in theories with tensor matter, extending beyond general relativity.

Findings

Universal form of initial constraints derived

Constraints for Einstein-aether theory obtained

Highlights differences from general relativity constraints

Abstract

In generally covariant metric gravity theories with tensor matter fields, the initial value constraint equations, unlike in general relativity, are in general not just the 0\mu-components of the metric field equation. This happens because higher derivatives can occur in the matter stress tensor. A universal form for these constraints is derived here from a generalized Bianchi identity that includes matter fields. As an application, the constraints for Einstein-aether theory are found.