Gravitational plane waves in Einstein-aether theory

TL;DR

This paper investigates gravitational plane wave solutions within Einstein-aether theory, revealing that such solutions exist only under specific parameter conditions and differ from general relativity.

Contribution

It systematically classifies the existence of gravitational plane wave solutions in Einstein-aether theory based on parameter choices, highlighting cases where solutions resemble or differ from general relativity.

Findings

Eight parameter cases identified for wave solutions

Two cases allow general gravitational plane waves

Six cases restrict wave forms or yield trivial solutions

Abstract

In this paper, we systematically study spacetimes of gravitational plane waves in Einstein-aether theory. Due to the presence of the timelike aether vector field, now the problem in general becomes overdetermined. In particular, for the linearly polarized plane waves, there are five independent vacuum Einstein-aether field equations for three unknown functions. Therefore, solutions exist only for particular choices of the four free parameters $c_{i}$'s of the theory. We find that there exist eight cases, in two of which any form of gravitational plane waves can exist, similar to that in general relativity, while in the other six cases, gravitational plane waves exist only in particular forms. Beyond these eight cases, solutions either do not exist or are trivial (simply representing a Minkowski spacetime with a constant or dynamical aether field.).