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arXiv · 1501.01244

First law and anisotropic Cardy formula for three-dimensional Lifshitz black holes

Eloy Ayon-Beato·Moises Bravo-Gaete·Francisco Correa·Mokhtar Hassaine·Maria Montserrat Juarez-Aubry·Julio Oliva
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Abstract

The aim of this paper is to confirm in new concrete examples that the semiclassical entropy of a three-dimensional Lifshitz black hole can be recovered through an anisotropic generalization of the Cardy formula derived from the growth of the number of states of a boundary non-relativistic field theory. The role of the ground state in the bulk is played by the corresponding Lifshitz soliton obtained by a double Wick rotation. In order to achieve this task, we consider a scalar field nonminimally coupled to new massive gravity for which we study different classes of Lifshitz black holes as well as their respective solitons, including new solutions for a dynamical exponent z=3. The masses of the black holes and solitons are computed using the quasilocal formulation of conserved charges recently proposed by Gim, Kim, Kulkarni and Yi and based on the off-shell extension of the ADT formalism. We confirm the anisotropic Cardy formula for each of these examples, providing a stronger base for its general validity. Consistently, the first law of thermodynamics together with a Smarr formula are also verified.

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Eloy Ayon-Beato, Moises Bravo-Gaete, Francisco Correa, Mokhtar Hassaine, Maria Montserrat Juarez-Aubry, Julio Oliva. 2017-08-04. First law and anisotropic Cardy formula for three-dimensional Lifshitz black holes. https://doi.org/10.1103/physrevd.91.064006

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