Smarr Formula and an Extended First Law for Lovelock Gravity

Details Smarr Formula and an Extended First Law for Lovelock Gravity Smarr Formula and an Extended First Law for Lovelock Gravity

2010-05-27

arxiv.org/abs/1005.5053v3

Class.Quant.Grav.27:235014,2010

Physics

High Energy Physics

High Energy Physics - Theory

20 pages; v2 - references added; v3 - includes important corrections to results

Scientific paper

10.1088/0264-9381/27/23/235014

We study properties of static, asymptotically AdS black holes in Lovelock gravity. Our main result is a Smarr formula that gives the mass in terms of geometrical quantities together with the parameters of the Lovelock theory. As in Einstein gravity, the Smarr formula follows from applying the first law to an infinitesimal change in the overall length scale. However, because the Lovelock couplings are dimensionful, we must first prove an extension of the first law that includes their variations. Key ingredients in this construction are the Killing-Lovelock potentials associated with each of the the higher curvature Lovelock interactions. Geometric expressions are obtained for the new thermodynamic potentials conjugate to variation of the Lovelock couplings.

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