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Title:  Energy extremality in the presence of a black hole 
Authors:  Sorkin, Rafael D. Varadarajan, Madhavan 
Issue Date:  1996 
Publisher:  Institute of Physics 
Citation:  Classical and Quantum Gravity, 1996, Vol.13, p19491969 
Abstract:  We derive the socalled first law of black hole mechanics for variations about stationary black hole solutions to the Einstein  Maxwell equations in the absence of sources. That is, we prove that 02649381/13/7/022/img6 where the black hole parameters M, 02649381/13/7/022/img7, A, 02649381/13/7/022/img8, J, V and Q denote mass, surface gravity, horizon area, angular velocity of the horizon, angular momentum, electric potential of the horizon and charge respectively. The unvaried fields are those of a stationary, charged, rotating black hole and the variation is to an arbitrary `nearby' black hole which is not necessarily stationary. Our approach is fourdimensional in spirit and uses techniques involving action variations and Noether operators. We show that the above formula holds on any asymptotically flat spatial 3slice which extends from an arbitrary cross section of the (future) horizon to spatial infinity. (Thus, the existence of a bifurcation surface is irrelevant to our demonstration. On the other hand, the derivation assumes without proof that the horizon possesses at least one of the following two (related) properties: (i) it cannot be destroyed by arbitrarily small perturbations of the metric and other fields which may be present, (ii) the expansion of the null geodesic generators of the perturbed horizon goes to zero in the distant future.) 
Description:  Restricted Access. An openaccess version is available at arXiv.org (one of the alternative locations) 
URI:  http://hdl.handle.net/2289/4613 
ISSN:  02649381 13616382 (online) 
Alternative Location:  http://arxiv.org/abs/grqc/9510031 http://dx.doi.org/10.1088/02649381/13/7/022 http://adsabs.harvard.edu/abs/1996CQGra..13.1949S 
Copyright:  1996, Institute of Physics 
Appears in Collections:  Research Papers (TP)

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