Thermodynamics of topological nonlinear charged Lifshitz black holes

TL;DR

This paper constructs new topological Lifshitz black holes with nonlinear electromagnetic fields, analyzes their thermodynamics, stability, and constraints on horizon topology, providing insights into their physical properties and stability conditions.

Contribution

It introduces a new class of analytic Lifshitz black holes with nonlinear charge, explores their thermodynamics, and examines their stability and horizon topology constraints.

Findings

Solutions exist only for certain horizon topologies due to charge reality conditions.

Thermodynamics satisfy the first law and a generalized Smarr formula.

Solutions are thermally stable within specific parameter ranges.

Abstract

In this paper, we construct a new class of analytic topological Lifshitz black holes with constant curvature horizon in the presence of power-law Maxwell field in four and higher dimensions. We find that in order to obtain these exact Lifshitz solutions, we need a dilaton and at least three electromagnetic fields. Interestingly enough, we find that the reality of the charge of the electromagnetic field which is needed for having solutions with curved horizon rules out black holes with hyperbolic horizon. Next, we study the thermodynamics of these nonlinear charged Lifshitz black holes with spherical and flat horizons by calculating all the conserved and thermodynamic quantities of the solutions. Furthermore, we obtain a generalized Smarr formula and show that the first law of thermodynamics is satisfied. We also perform a stability analysis in both canonical and grand-canonical ensemble. We find that the solutions are thermally stable in a proper ranges of the metric parameters. Finally, we comment on the dynamical stability of the obtained solutions under perturbations in four dimensions.