Smarr formula and an extended first law for Lovelock gravity

By David Kastor, Sourya Ray, Jennie Traschen. 2010

263 citations recorded by the source corpus.

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 higher curvature Lovelock interactions. Geometric expressions are obtained for the new thermodynamic potentials conjugate to the variation of the Lovelock couplings.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/146a7e4bd237e5d6eec219cfaba4f5bbbf74ec8f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Multiple reentrant phase transitions and triple points in Lovelock thermodynamics (2014, methodology): “For a black hole solution, characterized by mass M , charge Q, temperature T , and entropy S, the extended first law and the associated Smarr-Gibbs-Duhem relation read [57, 58] δM = TδS − 1 16πGN ∑”
Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization (2012, methodology): “[See also [26] for a generalization to the Lovelock gravities.”
Isolated critical point from Lovelock gravity (2014, background): “The thermodynamic potential to consider in the canonical ensemble is the Gibbs free energy, given by [21] (see also [22] for the Euclidean action calculation) α = − = G M TS G P T ( , , ).”
Extended phase space thermodynamics for third-order Lovelock black holes in diverse dimensions (2014, background): “A detailed discussion of extended first Law and Smarr formula for Lovelock gravity can be found in [40].”
Holographic black hole chemistry (2015, unknown): “Despite this fact [3, 24, 25] still find generalized Smarr relations to be valid even when higher curvature couplings are included as long as one treats the coefficients of the extra curvature terms as independent couplings which can be varied as well.”
Black hole chemistry: thermodynamics with Lambda (2016, methodology): “2.1 A brief review of standard black hole thermodynamics 2 2.2 History of variable Λ 4 2.3 Black hole chemistry 9 2.4 Lovelock gravity 9”