Gravitational Waves in Ghost Free Bimetric Gravity

TL;DR

This paper derives exact gravitational wave solutions in ghost free bimetric gravity, including vacuum and massive scalar modes, and explores their properties and stability within extended theories.

Contribution

It provides explicit gravitational wave solutions in ghost free bimetric gravity and analyzes their characteristics and stability in extended F(R) models.

Findings

Vacuum Brinkmann plane wave solutions exist for flat reference metric.

Massive scalar mode solutions are possible with proportional reference metric.

F(R) extensions admit similar solutions but often have ghost instabilities.

Abstract

We obtain a set of exact gravitational wave solutions for the ghost free bimetric theory of gravity. With a flat reference metric, the theory admits the vacuum Brinkmann plane wave solution for suitable choices of the coefficients of different terms in the interaction potential. An exact gravitational wave solution corresponding to a massive scalar mode is also admitted for arbitrary choice of the coefficients with the reference metric being proportional to the spacetime metric. The proportionality factor and the speed of the wave are calculated in terms of the parameters of the theory. We also show that a F(R) extension of the theory admits similar solutions but in general is plagued with ghost instabilities.