The radio halo in the merging cluster A3562

One of the possible sources of gamma-ray bursts (GRBs) are merging, compact neutronstar binaries. More than 90% of the binding energy of such a binary is released in the form of gravitational waves (GWs) in the last few seconds of the spiral-in phase before the formation of a black hole. In this article we investigate whether a fraction of this GW energy is transferred to magnetohydrodynamic waves in the magnetized plasma wind around the binary. Using the 3+1 orthonormal tedrad formalism, we study the propagation of a monochromatic, plane fronted, linearly polarized GW perpendicular to the ambient magnetic field in an ultra-relativistic wind, first in the comoving and then in the observer frame. A closed set of general relativistic magnetohydrodynamic (GRM) equations is derived in the form of conservation laws for electric charge, matter energy, momentum and magnetic energy densities. We linearize the GRM equations under the action of a monochromatic GW, which acts as a driver and find that fast magneto-acoustic waves grow, with amplitudes proportional to the GW amplitude and frequency and the strength of the background magnetic field.