Nonextensive statistics and the entropy on the horizon

We explore the application of nonextensive Bose statistics to describe the behavior of an ideal gas near the horizon of black holes, presenting a compelling case for its efficacy as an effective theory for interacting bosons. The central focus is on the careful selection of a nonextensive parameter, a critical aspect that enables the derivation of the correct entropy on the black hole horizon. Remarkably, this approach aligns with the well-established Bekenstein-Hawking entropy, showcasing the utility of nonextensive Bose statistics in capturing the thermodynamic properties of particles near black hole horizons. The study contributes to our understanding of fundamental interactions in extreme gravitational environments and provides a novel perspective on the statistical mechanics of black hole thermodynamics.