Thermodynamics of nonlinear charged Lifshitz black branes with hyperscaling violation

TL;DR

This paper explores the thermodynamics of hyperscaling violating Lifshitz black branes with nonlinear electromagnetic fields, deriving solutions, calculating energy, and analyzing stability, revealing that nonlinearity can induce instability.

Contribution

It provides analytic solutions for nonlinear charged Lifshitz black branes with hyperscaling violation and extends thermodynamic relations, including a generalized Smarr formula, with stability analysis.

Findings

Nonlinear electromagnetic fields affect black brane stability.

Derived energy density and thermodynamic relations for these solutions.

Identified conditions under which solutions become unstable.

Abstract

In this paper, we investigate the thermodynamics of hyperscaling violating Lifshitz black branes in the presence of a nonlinear massless electromagnetic field. We, first, obtain analytic nonlinear charged black brane solutions with hyperscaling violating factor in dilaton gravity and give the condition on the parameters of the metric for having black brane solutions. Second, we introduce the appropriate finite action in grand-canonical and canonical ensembles for nonlinear electromagnetic field. Next, by generalizing the counterterm method for the asymptotic Lifshitz spacetimes with hyperscaling violating factor, we calculate the energy density of our solutions. Then, we present a relation between the energy density and the thermodynamic quantities, electric potential, charge density, temperature and entropy density. This relation is the generalization of Smarr formula for anti-de Sitter black branes and charged Lifshiz solutions. Finally, we perform a stability analysis in both the canonical and grand-canonical ensemble. We show that the nonlinearity of electromagnetic field can make the solutions unstable in grand-canonical ensemble.