Topological and optical signatures of modified black-hole entropies

Ankit Anand; Kimet Jusufi; Spyros Basilakos; Emmanuel N. Saridakis

Paper

Topological and optical signatures of modified black-hole entropies

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, Rényi, 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 Rényi entropies yield a single unstable sector with global charge

, while logarithmic and Kaniadakis corrections produce canceling defects with

, 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

, 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.