Black Hole Thermodynamics and Stability in EYM Gravity with Quantum Fluctuation-Induced Corrections

We employ a mathematical technique known as the higher-dimensional Wu-Yang Ansatz to investigate a specific black hole solution within a five-dimensional (5D) geometrical context. This exploration is conducted within the framework of Einstein-Yang-Mills (EYM) theory, a synthesis of gravity and a specific force field. We thoroughly examine how the fundamental thermodynamic properties are affected by quantum fluctuations, coupled with logarithmic entropy corrections derived from the generalized uncertainty principle (GUP). These attributes encompass the black hole’s entropy, its ability to perform work, and its response to changes in temperature and pressure. Through a detailed analysis of the black hole’s specific heat capacity, a key thermodynamic quantity, we conduct a comprehensive examination of its stability, aiming to discern any potential phase transitions. Intriguingly, our investigation reveals the black hole’s remarkable stability persists, even under the influence of these quantum fluctuations.