Critical Behavior of Photon Rings in Kerr-Bertotti-Robinson Spacetime

TL;DR

This paper studies how magnetic fields influence photon rings around rotating black holes, revealing observable modifications in ring structure that can help probe black hole environments.

Contribution

It introduces a detailed analysis of photon ring behavior in Kerr-Bertotti-Robinson spacetime, highlighting magnetic field effects on geodesic structure and photon ring observables.

Findings

Magnetic fields alter the geodesic structure of photon orbits.

Photon ring parameters depend on black hole spin, magnetic field, and observer angle.

Higher-order images are affected by near-critical lensing equations.

Abstract

In this work, we investigate the critical behavior of photon rings in the Kerr-Bertotti-Robinson spacetime, describing a rotating black hole immersed in a background magnetic field. We analyze the radial and angular motions of photons under the small magnetic field approximation. Focusing on unstable spherical orbits, we determine three key parameters, $\gamma$, $\delta$, and $\tau$, which characterize radial compression, azimuthal advancement, and time delay. We then examine how these parameters depend on the black hole spin, magnetic field strength, and observer inclination for both on-axis and off-axis observers, and we further analyze the properties of higher-order images through near-critical lens equations. The results show that the magnetic field modifies the geodesic structure, and leads to observable changes in the fine structure of photon rings, providing a useful framework for probing magnetized black hole environments.