The electromagnetic signature of black hole ring-down

We investigate the generation of electromagnetic radiation by gravitational waves interacting with a strong magnetic field in the vicinity of a vibrating Schwarzschild black hole. Such an effect may play an important role in gamma-ray bursts, supernovae, and in particular their afterglows. It may also provide an electromagnetic counterpart to gravity waves in many situations of interest, enabling easier extraction and verification of gravity wave waveforms from gravity wave detection. We set up the Einstein-Maxwell equations for the case of odd-parity gravity waves impinging on a static magnetic field as a covariant and gauge-invariant system of differential equations that can be integrated as an initial-value problem or analyzed in the frequency domain. We numerically investigate both of these cases. We find that the black hole ring-down process can produce substantial amounts of electromagnetic radiation from a dipolar magnetic field in the vicinity of the photon sphere.