Energy extremality in the presence of a black hole

Sorkin, Rafael D.; Varadarajan, Madhavan

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/4613

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DC Field	Value	Language
dc.contributor.author	Sorkin, Rafael D.	-
dc.contributor.author	Varadarajan, Madhavan	-
dc.date.accessioned	2012-06-04T08:30:19Z	-
dc.date.available	2012-06-04T08:30:19Z	-
dc.date.issued	1996	-
dc.identifier.citation	Classical and Quantum Gravity, 1996, Vol.13, p1949-1969	en
dc.identifier.issn	0264-9381	-
dc.identifier.issn	1361-6382 (online)	-
dc.identifier.uri	http://hdl.handle.net/2289/4613	-
dc.description	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)	en
dc.description.abstract	We derive the so-called 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 0264-9381/13/7/022/img6 where the black hole parameters M, 0264-9381/13/7/022/img7, A, 0264-9381/13/7/022/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 four-dimensional in spirit and uses techniques involving action variations and Noether operators. We show that the above formula holds on any asymptotically flat spatial 3-slice 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.)	en
dc.language.iso	en	en
dc.publisher	Institute of Physics	en
dc.relation.uri	http://arxiv.org/abs/gr-qc/9510031	en
dc.relation.uri	http://dx.doi.org/10.1088/0264-9381/13/7/022	en
dc.relation.uri	http://adsabs.harvard.edu/abs/1996CQGra..13.1949S	en
dc.rights	1996, Institute of Physics	en
dc.title	Energy extremality in the presence of a black hole	en
dc.type	Article	en
Appears in Collections:	Research Papers (TP)

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