The evolution of a warped disc around a Kerr black hole

We consider the evolution of a warped disc around a Kerr black hole, under conditions such that the warp propagates in a wave-like manner. This occurs when the dimensionless effective viscosity, alpha, that damps the warp is less than the characteristic angular semi-thickness, H / R, of the disc. We adopt linearized equations that are valid for warps of sufficiently small amplitude in a Newtonian disc, but also account for the apsidal and nodal precession that occur in the Kerr metric. Through analytical and time-dependent studies, we confirm the results of Demianski & Ivanov and of Ivanov & Illarionov, that such a disc takes on a characteristic warped shape. The inner part of the disc is not necessarily aligned with the equator of the hole, even in the presence of dissipation. We draw attention to the fact that this might have important implications for the directionality of jets emanating from discs around rotating black holes.