Gravitational Waves and Electromagnetic Radiation from Charged Black Hole Binaries

In this manuscript, we investigate the electromagnetic radiation of a binary system of electrically charged black holes. Using the results of previous works, we compute the analytical expression for the waveform, the phase, and the Fourier transform during the inspiral phase for both the electromagnetic and gravitational radiations. To do so, we consider the quasi-circular approximation and small values for the charge-to-mass ratio in each black hole. In the case of electromagnetic radiation, we focus on the dipole contribution, but we also include the quadrupole term to complete our discussion. We found that the gravitational and electromagnetic waveforms contain two terms, and so does the Fourier transform. However, the behavior is dominated only by one of them. In the frequency-domain waves, for example, the dipole and quadrupole contributions and the gravitational wave are dominated by terms proportional to f(-3/6), f(-1/6), and f(-7/6), respectively. As expected, the gravitational radiation and the quadrupole contribution have the same phase, in contrast to the dipole contribution. Moreover, the electromagnetic wave is more sensitive to changes in the charge-to-mass ratio than the gravitational wave.