Applications of metric perturbations of a rotating black hole: distortion of the event horizon

The influence of matter perturbations on the horizon of a rotating black hole is studied. The perturbation at the horizon is completely characterized by appropriately defined horizon multipole moments (HMM's) which are related to the number flux of quanta across the horizon. These HMM's are evaluated for several cases of interest. Specifically, it is shown that for an extreme Kerr black hole ($a=M$) a ring of matter on the marginally stable circular orbit has no tidal influence on the black hole. On the other hand, a single test particle on the same orbit does raise a tide on the horizon although it does not radiate gravitational waves. Finally, the spin-down law for a black hole in the presence of a distant stationary non-axially symmetric moon is derived.