Black Hole Perturbations and Electric-Magnetic Duality

Black holes can be electromagnetically charged, or carry vector charge from new fundamental fields. Their response to small fluctuations is of paramount importance to study gravitational wave generation. However, the usual even and odd sectors of gravitoelectromagnetic waves couple if the black hole is magnetically charged, a fact that complicates significantly the perturbative approach. In this paper, perturbation theory based on harmonic expansion is extended to have manifest invariance under electric-magnetic duality. As a result, the equations decouple into two generalised even and odd sectors, each governed by master wave equations that include the most general coupling to a dyonic source. These can be used to compute, in a simple manner, the gravitational and electromagnetic radiation emitted in the interaction of the most general spherically symmetric black holes of the Einstein--Maxwell theory with electromagnetically charged matter.