Propagation of gravitational waves in multimetric gravity

TL;DR

This paper analyzes gravitational wave propagation in multimetric gravity theories, showing they travel at light speed and can have multiple polarization states, with implications for testing these theories via gravitational wave observations.

Contribution

It provides a comprehensive analysis of gravitational wave polarizations in multimetric gravity, including a specific model example, expanding understanding of wave signatures in such theories.

Findings

Gravitational waves propagate at the speed of light in multimetric theories.

Number of polarization states varies from two to six depending on model parameters.

A specific multimetric model allows only two tensor polarizations, similar to general relativity.

Abstract

We discuss the propagation of gravitational waves in a recently discussed class of theories containing N >= 2 metric tensors and a corresponding number of standard model copies. Using the formalism of gauge-invariant linear perturbation theory we show that all gravitational waves propagate at the speed of light. We then employ the Newman-Penrose formalism to show that two to six polarizations of gravitational waves may exist, depending on the parameters entering the equations of motion. This corresponds to E(2) representations N_2, N_3, III_5 and II_6. We finally apply our general discussion to a recently presented concrete multimetric gravity model and show that it is of class N_2, i.e., it allows only two tensor polarizations, as it is the case for general relativity. Our results provide the theoretical background for tests of multimetric gravity theories using the upcoming gravitational wave experiments.