Thermodynamic instability of topological black holes with nonlinear source

TL;DR

This paper explores higher-dimensional topological black holes with nonlinear electrodynamics, analyzing their thermodynamic properties, stability, and effects of rotation, revealing thermodynamic instability under certain conditions.

Contribution

It provides new solutions for topological black holes with nonlinear sources and examines their thermodynamic behavior and stability in various ensembles.

Findings

Solutions satisfy the first law of thermodynamics

Rotating solutions' conserved quantities calculated using counterterm method

Stability depends on ensemble and parameters

Abstract

In this paper, we obtain higher dimensional topological black hole solutions of Einstein-$\Lambda$ gravity in the presence of a class of nonlinear electrodynamics. First, we calculate the conserved and thermodynamic quantities of ($n+1$)-dimensional asymptotically flat solutions and show that they satisfy the first law of thermodynamics. Also, we investigate the stability of these solutions in the (grand) canonical ensemble. Second, we endow a global rotation to the static Ricci-flat solutions and calculate the conserved quantities of solutions by using the counterterm method. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the electric charge, and show that these quantities satisfy the first law of thermodynamics. Then, we perform a stability analysis of the rotating solutions both in the canonical and the grand canonical ensembles.