Thermodynamics of Rotating Lovelock-Lifshitz Black Branes

TL;DR

This paper explores the thermodynamic properties and stability of rotating Lovelock-Lifshitz black branes, deriving key relations and analyzing stability conditions based on dynamical critical exponent and spacetime dimensions.

Contribution

It provides new thermodynamic relations, including a Smarr-type formula, and analyzes stability criteria for these black branes in different ensembles.

Findings

Thermodynamic quantities satisfy the first law.

Solutions are stable for z ≤ n-1.

Potential instability for z > n-1.

Abstract

We investigate the thermodynamics of rotating Lovelock-Lifshitz black branes. We calculate the conserved and thermodynamic quantities of the solutions and obtain a relation between temperature, angular velocity, energy density, entropy density and angular momentum density. We, also, obtain a Smarr-type formula for the energy density as a function of entropy and angular momentum densities, and show that the thermodynamic quantities calculated in this paper satisfy the first law of thermodynamics. Finally, we investigate the stability of black brane solutions in both canonical and grand-canonical ensemble. We find that the solutions are thermally stable for the solutions with $z\leq n-1$, while they can be unstable for $z>n-1$.