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arXiv · 2512.13769

Topological and optical signatures of modified black-hole entropies

Ankit Anand·Kimet Jusufi·Spyros Basilakos·Emmanuel N. Saridakis
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Abstract

We investigate how deviations from the Bekenstein-Hawking entropy modify black-hole spacetimes through the recently proposed entropy-geometry correspondence. For four representative modified entropies, namely Barrow, R\'enyi, Kaniadakis, and logarithmic, we derive the corresponding effective metrics and analyze their thermodynamic and topological classification using the off-shell free energy and winding numbers. We show that Barrow and R\'enyi entropies yield a single unstable sector with global charge $W=-1$, while logarithmic and Kaniadakis corrections produce canceling defects with $W=0$, revealing topological structures absent in the Schwarzschild case. Using the modified metrics, we further calculate the photon-sphere radius and shadow size, showing that each modified entropy relation induces characteristic optical shifts. Thus, by comparing with Event Horizon Telescope observations of Sgr A$^\ast$, we extract new bounds on all entropy-deformation parameters. Our results demonstrate that thermodynamic topology, together with photon-sphere phenomenology, offers a viable way to test generalized entropy frameworks and probe departures from the Bekenstein-Hawking area law.

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Ankit Anand, Kimet Jusufi, Spyros Basilakos, Emmanuel N. Saridakis. 2025-12-15. Topological and optical signatures of modified black-hole entropies. https://doi.org/10.1140/epjc%2Fs10052-026-15365-0

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