Rotating hairy black holes and thermodynamics from gravitational decoupling

TL;DR

This paper develops a method to construct rotating hairy black hole solutions using gravitational decoupling, analyzes their thermodynamics, and finds stability conditions depending on hairy parameters and spin.

Contribution

It introduces a novel approach combining gravitational decoupling with Newman-Janis and Azreg-A"{i}nou algorithms to generate rotating hairy black holes and studies their thermodynamic properties.

Findings

Small hairy black holes are more thermodynamically stable.

Horizon radius and temperature ranges depend non-trivially on hairy parameters.

Rotating hairy black holes can achieve thermodynamic equilibrium under certain conditions.

Abstract

We study the method of extended gravitational decoupling in obtaining static black hole solutions satisfying Einstein's equations with a tensor vacuum. The source has quite generic characteristics and satisfies the strong energy condition. The stationary, axisymmetric counterpart of the static metric is obtained by applying the Newman-Janis and Azreg-A\"{i}nou algorithms. The thermodynamics of the rotating solution is studied and the expressions of various thermodynamic quantities are derived. The dependence of the temperature, free energy and specific heat on the horizon radius is studied for various values of the hairy parameter and the black hole spin. Such a study reveals that small hairy black holes are thermodynamically more stable compared to large hairy black holes, and that the horizon radius and temperature range for which the rotating hairy black holes can be in thermodynamic equilibrium with the surroundings depends non-trivially on the hairy parameters. We further discuss the first law of black hole thermodynamics for the hairy case and discuss its implications.