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

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 theo...

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Bibliographic Details
Published in:arXiv.org 2017-08
Main Authors: Ayon-Beato, Eloy, Bravo-Gaete, Moises, Correa, Francisco, Hassaine, Mokhtar, Maria Montserrat Juarez-Aubry, Oliva, Julio
Format: Article
Language:English
Subjects:
Anisotropy
Black holes
Energy conservation law
Field theory
Relativistic theory
Solitary waves
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1501.01244