Black hole thermodynamics via Tsallis statistical mechanics and phase transitions probed by optical characteristics
Year: 2026
Type: article
Abstract: We establish a statistically grounded framework for generalized black hole thermodynamics based on non-extensive statistics. Unlike conventional phenomenological approaches, we explicitly derive a structurally unique generalized Bekenstein–Hawking entropy from the microscopic state counting of a near-horizon photon gas within the framework of Tsallis statistics. This formulation is fully consistent with the first law of black hole thermodynamics and smoothly recovers the standard Bekenstein–Hawking area law in the extensive limit ( q → 1 ). To examine the macroscopic viability of this microscopically grounded entropy, we investigate its implications for Reissner–Nordström black holes. We demonstrate that the entropic deformation governs both local and global thermal stability, thereby generating a rich multi-branched phase structure comprising small, intermediate, and large black holes with Van der Waals-like critical behavior. We further establish an optical-thermodynamic analogy by relating photon-sphere observables, including orbital periods and Lyapunov exponents, to thermodynamic variables. These optical signatures qualitatively track the thermodynamic critical behavior and phase structure, suggesting their potential relevance as observational probes in future high-resolution measurements. Collectively, these results may shed light on a conceptual connection between non-extensive entropy, black-hole critical phenomena, and strong-gravity optics.
Source: Classical and Quantum Gravity
Institutions: Naresuan University, Ramkhamhaeng University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7160290632