Thermal analysis of gravitational decoupling black hole solution

In this work, we examine the thermodynamic properties of the hairy black holes that develop when the Reissner–Nordström geometry is applied to the gravitational decoupling method. Gibbs free energy and energy emission are also examined in our investigation. We compute several parameters to evaluate the local and global thermodynamic stability, including the Hawking temperature, geometric mass, and heat capacity. The first law of thermodynamics calculates the black hole's temperature and assesses the energy emission rate. We investigate the black hole's phase transition behavior by calculating the Gibbs free energy, paying particular attention to the swallowing tails.