Phenomenological model for the electromagnetic response of a black hole binary immersed in magnetic field

Electromagnetic counterparts of gravitational wave events usually involve neutron stars during compact binary coalescences. On the other hand, the community generally believes that electromagnetic emissions are hardly generated during the mergers of binary black holes. Nevertheless, some authors have considered the possibility of an EM counterpart signal after the GW150914, opening the opportunity to investigate the electromagnetic emission of stellar-mass black holes (BHs) mergers. In the case of black holes in a strong magnetic field or with electric charges, electromagnetic emissions would appear accompanied by gravitational waves. In this work, based on the membrane paradigm, we consider a phenomenological model to study the electromagnetic radiation generated by binary black holes surrounded by a uniform magnetic field. We obtain the electromagnetic waveform detected by a far-distance observer for varied black hole spins. By analytical Fourier transformation, we get the chirp property of the electromagnetic waves; we found that the power-law is 5/6, which has the opposite sign compared to gravitational waves. The frequency of such electromagnetic waves is the same as gravitational waves.