Thermal stability and effects of thermal fluctuations on the static and spherically symmetric hairy black hole by gravitational decoupling

Abstract

In this paper, we explore the thermodynamic aspects of the hairy black hole solution developed by gravitational decoupling in the spherical symmetry, considering its energy emission, Gibbs free energy, and thermal fluctuations. Our analysis involves the calculation of various quantities, including the Hawking temperature, geometric mass, and heat capacity to discuss the thermodynamic stability at local and global scales. To determine the temperature of the black hole, we utilize the first law of thermodynamics. Additionally, we evaluate the energy emission rate and establish its proportionality to the decoupling parameter α. By calculating the Gibbs free energy, we investigate the phase transition behavior through the swallowing tails of the hairy black holes. Furthermore, we derive the corrected entropy to examine the impact of thermal fluctuations on small and large black holes. We also calculated horizon radius r0, inner stable circular orbit rISCO , photon sphere radius rph, and shadows radius Rsh. Remarkably, the length scale parameters α (decoupling parameter) and β exhibit substantial influences on the thermodynamic properties of under consideration hairy black holes.