Conformal Killing horizons

Abstract

For time dependent black hole space–times the event horizon cannot be described by a Killing horizon. In the case when the space–time admits a timelike conformal Killing field, which becomes null on a boundary called the conformal stationary limit surface, one can locally describe the expanding event horizon by using this boundary, provided that it is a null geodesic hypersurface. In this case the boundary is called a conformal Killing horizon and is shown to be null and geodesic if and only if the twist of the conformal Killing trajectories on the hypersurface vanishes. Moreover if the space–time is conformally related to a stationary asymptotically flat black hole space–time, it is shown that this hypersurface is globally equivalent to the event horizon, provided that the conformal factor goes to a constant at null infinity. When the conformal stationary limit surface does not coincide with the conformal Killing horizon, a generalization of the weak rigidity theorem which establishes the conformal Killing property of the event horizon and the rigidity of its rotation is obtained. A physical definition of surface gravity for conformal Killing horizons is given, which is then used to formulate a generalized zeroth law of black hole physics.