Exploring non-perturbative corrections in thermodynamics of static dirty black holes

This research delves into an extensive exploration of the thermodynamic characteristics exhibited by a contaminated black hole subject to a uniform electric field, within the theoretical framework of the EinsteinNonlinear Electrodynamics (ENE)-dilaton theory. The investigation encompasses a thorough analysis of diverse thermodynamic facets, encompassing heat capacity, Helmholtz free energy, and internal energy. Through this comprehensive examination, valuable insights are provided into the distinctive behavior of the black hole when subjected to the influence of the electric field. Moreover, our study embarks on an exploration of the nuanced interplay between quantum effects and the thermodynamic profile, with a particular focus on scrutinizing the quantum-corrected entropy. This approach allows for a deeper understanding of the intricate relationship between quantum mechanics and the thermodynamic attributes exhibited by the system. By doing so, we aim to illuminate the non-perturbative corrections inherent in this intricate system, thereby contributing to a holistic comprehension of the altered thermodynamics characterizing dirty black holes within the confines of the specified theoretical framework. In essence, this research endeavors to uncover the subtleties of the modified thermodynamic landscape governing black holes tainted by external factors, specifically within the context of the ENE-dilaton theory. The outcomes of this study promise to extend our understanding of the intricate interactions within such complex systems, offering valuable insights into the non-perturbative corrections that manifest in their thermodynamic behavior.