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arXiv · 2606.14815

Perturbative and Non-Perturbative Contributions to Black Hole Thermodynamics with String Clouds and Dark Matter Backgrounds

Kumar Sambhav Upadhyay·Sudhaker Upadhyay·Bhabani Prasad Mandal
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Abstract

We investigate the effects of perturbative and non-perturbative quantum corrections on the thermodynamics of black holes immersed in a perfect fluid dark matter (PFDM) background with a cloud of strings (CoS) in asymptotically anti-de Sitter spacetime. Starting from the Bekenstein-Hawking entropy as the semiclassical baseline, we incorporate two distinct classes of corrections arising from small thermal fluctuations about thermodynamic equilibrium. In the perturbative sector, we derive the logarithmically corrected entropy and systematically compute the resulting modifications to the mass, Helmholtz free energy, Gibbs free energy, heat capacity, and pressure. The stability structure of the system is analyzed through the sign behavior of the heat capacity, which reveals a transition from a thermodynamically unstable to a stable phase. In the non-perturbative sector, we introduce exponential corrections to the entropy and carry out a parallel analysis of all thermodynamic quantities. We demonstrate that non-perturbative effects are negligible for large black holes but become significant as the horizon radius shrinks toward the Planck regime. In both sectors, we investigate the equation of state and search for a van der Waals-like critical point by examining the simultaneous vanishing of the first and second pressure derivatives with respect to thermodynamic volume; no such inflection point is found within the physically admissible domain. Our results illuminate the contrasting roles of logarithmic and exponential entropy corrections in governing the thermodynamic stability and phase structure of PFDM black holes with a CoS.

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Kumar Sambhav Upadhyay, Sudhaker Upadhyay, Bhabani Prasad Mandal. 2026-06-12. Perturbative and Non-Perturbative Contributions to Black Hole Thermodynamics with String Clouds and Dark Matter Backgrounds. https://arxiv.org/abs/2606.14815

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