Godel Type Metrics in Einstein-Aether Theory

TL;DR

This paper demonstrates that G"odel-type metrics, which are solutions in general relativity, also solve Einstein-Aether theory equations, with specific parameter constraints, linking Lorentz violation to known solutions.

Contribution

It shows G"odel-type metrics are exact solutions in Einstein-Aether theory, expanding understanding of solutions in Lorentz-violating gravity models.

Findings

G"odel-type metrics are solutions in Einstein-Aether theory.

The solutions satisfy Maxwell field equations.

Parameter constraints include c1 - c3 = 1.

Abstract

Aether theory is introduced to implement the violation of the Lorentz invariance in general relativity. For this purpose a unit timelike vector field introduced to theory in addition to the metric tensor. Aether theory contains four free parameters which satisfy some inequalities in order that the theory to be consistent with the observations. We show that the G{\" o}del type of metrics of general relativity are also exact solutions of the Einstein-aether theory. The only field equations are the 3-dimensional Maxwell field equations and the parameters are left free except $c_{1}-c_{3}=1$.