First law and anisotropic Cardy formula for three-dimensional Lifshitz black holes
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.
Keywords
Cite
@article{arxiv.1501.01244,
title = {First law and anisotropic Cardy formula for three-dimensional Lifshitz black holes},
author = {Eloy Ayon-Beato and Moises Bravo-Gaete and Francisco Correa and Mokhtar Hassaine and Maria Montserrat Juarez-Aubry and Julio Oliva},
journal= {arXiv preprint arXiv:1501.01244},
year = {2017}
}