Propagation of gravitational waves in multimetric gravity

We discuss the propagation of gravitational waves in a recently discussed class of theories containing $N\ge 2$ 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 field equations. This corresponds to E(2) representations $N_2$, $N_3$, ${\mathrm{III}}_5$ and ${\mathrm{II}}_6$. 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.