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Zbl 1064.83015
Sultana, J.; Dyer, C.C.
Conformal Killing horizons. (English)
[J] J. Math. Phys. 45, No. 12, 4764-4776 (2004). ISSN 0022-2488; ISSN 1089-7658/e

Summary: 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.

MSC 2000:: *83C30 Asymptotic procedures (general relativity)

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