Gravitational waves and electromagnetic radiation from charged black hole binaries

It is still an open issue if astrophysical black holes have electric charges or not. In this work, we analytically calculate gravitational and electromagnetic waveforms in the frequency domain for charged black hole binaries during the inspiral phase. In addition to the well-known $f^{-7\mathrm{/}6}$ waveforms, we also get a $-11\mathrm{/}6$ power law gravitational wave component. The phase of waveforms for charged binary is fully derived. In the case of electromagnetic counterparts, we focus on the electromagnetic dipole radiation, but we include the quadrupole contribution to complete our discussion. We also obtain the chirp property of the electromagnetic waves. In the case of dipole radiation, the frequency-domain waves are proportional to $f^{-7\mathrm{/}6}$, while $f^{-1\mathrm{/}6}$ appears in the quadrupole contribution. The frequency-domain waveforms can be used to estimate the charges of black holes in the current gravitational wave observations.