Metric Redefinitions in Einstein-Aether Theory

TL;DR

This paper explores how redefining the metric and vector field in Einstein-Aether theory alters coupling constants, simplifying the analysis of solutions and aiding the study of Lorentz violation in a covariant framework.

Contribution

It introduces a metric and vector field redefinition in Einstein-Aether theory that changes coupling constants, allowing one to be set to zero for simplified solution analysis.

Findings

Reparameterization affects coupling constants in the theory.

One coupling constant can be eliminated through redefinition.

Simplifies the study of Einstein-Aether solutions.

Abstract

`Einstein-Aether' theory, in which gravity couples to a dynamical, time-like, unit-norm vector field, provides a means for studying Lorentz violation in a generally covariant setting. Demonstrated here is the effect of a redefinition of the metric and vector field in terms of the original fields and two free parameters. The net effect is a change of the coupling constants appearing in the action. Using such a redefinition, one of the coupling constants can be set to zero, simplifying studies of solutions of the theory.