Thermodynamics of charged Lifshitz black holes with quadratic corrections

TL;DR

This paper derives and analyzes four classes of charged Lifshitz black hole solutions with quadratic curvature corrections, examining their thermodynamics and mass properties in arbitrary dimensions.

Contribution

It introduces four new classes of charged Lifshitz black hole solutions with quadratic corrections and verifies their thermodynamic consistency.

Findings

Three solutions are extremal with zero mass.

The last solution's mass and charge depend on an integration constant.

The first law of thermodynamics and Smarr formula are confirmed for all solutions.

Abstract

In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric function is shown to depend on a unique integration constant. The masses of these solutions are computed using the quasilocal formalism based on the relation established between the off-shell ADT and Noether potentials. Among these four solutions, three of them are interpreted as extremal in the sense that their mass vanishes identically. For the last family of solutions, the quasilocal mass and the electric charge both are shown to depend on the integration constant. Finally, we verify that the first law of thermodynamics holds for each solution and a Smarr formula is also established for the four solutions.