Photon Spheres and shadow of modified black-hole entropies

TL;DR

This paper links modified black hole entropy to observable optical features like photon spheres and shadows, enabling tests of entropy corrections via astronomical data.

Contribution

It establishes a direct relation between entropy corrections and metric functions, and uses observational data to constrain these modifications.

Findings

Different entropy corrections cause measurable shifts in photon sphere and shadow size.

Comparison with Sgr A* data constrains parameters of entropy correction models.

Provides a method to test generalized entropy frameworks using black hole imaging.

Abstract

Starting from the first law of black hole thermodynamics, we establish an explicit correspondence between the corrected entropy and the metric function under the condition of fixed black hole energy and horizon position. Using the corrected metric, we further compute the photon sphere radius and shadow size, demonstrating that different entropy corrections lead to characteristic optical shifts. By comparing with the Event Horizon Telescope observations of Sgr A*, we constrain the parameter range introduced in the corrected entropy. This provides a feasible approach for testing generalized entropy frameworks and probing deviations from the Bekenstein-Hawking area law.