Thermodynamics of non-linearly charged Anti-de Sitter black holes in four-dimensional Critical Gravity

TL;DR

This paper introduces new four-dimensional Anti-de Sitter black hole solutions in Critical Gravity with nonlinear electrodynamics, analyzing their thermodynamics and stability, marking the first such charged solutions with non-zero thermodynamic quantities.

Contribution

It presents novel charged black hole solutions in four-dimensional Critical Gravity with nonlinear electrodynamics, including their thermodynamic properties and stability analysis.

Findings

Existence of black holes with horizons in Critical Gravity.

Thermodynamical quantities are non-zero, unlike previous solutions.

Solutions satisfy first law of thermodynamics and Smarr formula.

Abstract

In this work, we provide new examples of Anti-de Sitter black holes with a planar base manifold in four-dimensional Critical Gravity by considering nonlinear electrodynamics as a matter source. We find a general solution characterized by the presence of only one integration constant where, for a suitable election of coupling constants, we can show the existence of one or more horizons. Additionally, we compute its non-null thermodynamical quantities through a variety of techniques, testing the validity of the first law of thermodynamics as well as a Smarr formula. Finally, we analyze the local thermodynamical stability of the solutions. To our knowledge, these charged configurations are the first example with Critical Gravity where their thermodynamical quantities are not zero.