# The shadows and photon rings of two minimal deformations of Schwarzschild black holes

## TL;DR

This study analyzes the optical features of two minimal Schwarzschild black hole deformations, examining their shadows, photon rings, and intensities under various accretion models, and proposes a method to distinguish them.

## Contribution

It introduces a comparative analysis of Kazakov-Solodukhin and Ghosh-Kumar black holes' optical properties and suggests a way to differentiate them using thin disk models.

## Key findings

- Kazakov-Solodukhin black hole shadow size increases with quantum correction.
- Ghosh-Kumar black hole shadow size decreases and brightness varies with magnetic charge.
- Photon rings are narrower for Kazakov-Solodukhin and wider for Ghosh-Kumar black holes.

## Abstract

This paper primarily investigates the optical characteristics of two minimal Schwarzschild black hole deformations, the Kazakov-Solodukhin and Ghosh-Kumar black holes, under different accretion models. The event horizon, photon sphere, and critical impact parameter of the former increase compared with the Schwarzschild black hole, but those of the latter decrease. The data from the Event Horizon Telescope Collaboration are used to constrain the parameter ranges of the two black holes. In the case of spherical accretion, the quantum correction of Kazakov-Solodukhin black hole leads to the increase of black hole shadow size and the decrease of integrated intensity, while the shadow size of magnetically charged Ghosh-Kumar black hole decreases and the integrated intensity increases. The shadow radius of the black hole is independent of the spherical accretion models. For an optically and geometrically thin accretion disk, the integrated intensity is mainly contributed by direct emission, and the contributions of photon rings and lensed rings are very small. In addition, the photon rings and lensed rings of Kazakov-Solodukhin black hole are narrower, while those of Ghosh-Kumar black hole are wider. Whereas the Kazakov-Solodukhin black hole exhibits higher brightness, the Ghosh-Kumar black hole shows lower brightness. Additionally, a disk closer to the black hole correlates with a smaller shadow radius. This paper proposes a method to distinguish different black holes in a specific thin disk model.