The dynamics of static hairy black holes and thermodynamics through gravitational decoupling in quantum space

Abstract

In this study, we explore various essential aspects of a noncommutative theory that incorporates space deformation. Through the Extended Gravitational Decoupling (EGD) approach within the Strong Energy Condition (SEC), we investigate the gravitational decoupling method to obtain static black hole solutions that satisfy Einstein’s field equations with a vacuum tensor. The analysis concentrates on the thermodynamics of the static solution, examining and deriving expressions for various thermodynamic quantities. This investigation explores how temperature, free energy, and specific heat depend on the horizon radius, considering different values for both hairy and noncommutative parameters. The study suggests that thermodynamically, smaller hairy black holes exhibit greater stability compared to larger ones. It also reveals a nontrivial relationship between the horizon radius, temperature range, and specific values of the hairy parameters for static hairy black holes when considered in thermodynamic equilibrium with their Hawking radiation. The discussion extends to the implications of the first law of black hole thermodynamics in the context of the noncommutative hairy case.