The aether-modified gravity and the Godel metric

TL;DR

This paper explores a modified gravity theory incorporating Lorentz-breaking aether terms, demonstrating that the G"odel metric remains a solution under certain conditions and analyzing the effects of these modifications.

Contribution

It formulates a nonminimal aether-modified gravity theory and investigates its solutions, particularly the G"odel metric, revealing how Lorentz-breaking terms influence classical solutions.

Findings

G"odel metric solves the modified Einstein equations with aether terms.

Small Lorentz-breaking corrections lead to usual matter content.

Aether terms modify the G"odel metric when matter is unchanged.

Abstract

We formulate the nonminimal aether-modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the CPT-even Lorentz-breaking aether-like gravity term proposed by Carroll. For this theory, we show that the G\"{o}del metric solves the modified Einstein equations under a corresponding modification of the matter, while, for the small Lorentz-breaking corrections, the matter turns out to be usual. On the other side, if the matter is suggested to be the same as in the usual general relativity, the G\"{o}del metric is modified by additive aether terms.