Dynamical black holes

Abstract

For time dependent black hole spacetimes the event horizon cannot be described by a Killing horizon. We show that when the spacetime admits a time like conformal Killing field which generates a hypersurface, called the conformal Killing horizon (CKH), one can locally describe the event horizon by using this hypersurface. When the CKH does not coincide with the conformal stationary limit surface, on which the conformal Killing field becomes null, 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 CKHs is given, which is then used to formulate a generalized zeroth law of black hole physics.