Gravitoelectromagnetic quadrirefringence

We develop an effective approach for the study of the interaction of gravitational waves (GWs) and electromagnetic waves (EMWs), showing that quadrirefringence can be produced, a phenomenon consisting in a frequency and polarization dependency of the speed of the different polarizations of GWs and EMWs, which is also inducing a frequency and polarization dependent modification of the GW-EMW luminosity distance ratio. Quadrirefringence can be due to the GW-EMW interaction in the source or during the propagation from the source to the observer. In the first case the astrophysical properties of the source can induce a unique characteristic imprint on GWs and EMWs for each source, the rainbow of binaries, while the effect on the propagation from the source could be used to probe the large scale electromagnetic field using GWs. Numerical general relativistic magnetohydrodynamic (GRMHD) simulations can be used to obtain precise theoretical predictions for different binary systems with large electromagnetic and gravitational fields, such as binary neutron stars.