Deviations from Kerr: Polar critical curves and photon rings in a class of separable spacetimes
Abstract
Black-hole critical curves and photon rings provide complementary probes of strong-field geometry, motivating a unified analytic description of these observables beyond Kerr and a direct comparison with the Kerr predictions. We develop such a description for polar observers in a radial class of stationary, axisymmetric spacetimes with separable null geodesics. The spacetime dependence is organized through natural optical combinations selected by the null dynamics and a Kerr-relative representation suited to weak deviations from Kerr. We derive compact exact expressions for the polar critical radius, Lyapunov exponent, time delay, and rotation parameter, together with general first-order formulas that can be applied once the deformation functions of a specific metric are supplied. The weak-deviation analysis shows that the combined polar observables probe only a finite set of local deformation values and radial derivatives at the critical orbit, rather than the full radial profiles.
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BibTeX
@misc{yan2026deviations,
title = {{Deviations from Kerr: Polar critical curves and photon rings in a class of separable spacetimes}},
author = {Hao-Peng Yan and Xiang-Qian Li and Xiao-Jun Yue},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01290},
eprint = {2609.01290},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01290},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Deviations from Kerr: Polar critical curves and photon rings in a class of separable spacetimes
AU - Hao-Peng Yan
AU - Xiang-Qian Li
AU - Xiao-Jun Yue
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01290
UR - https://arxiv.org/abs/2609.01290
AB - Black-hole critical curves and photon rings provide complementary probes of strong-field geometry, motivating a unified analytic description of these observables beyond Kerr and a direct comparison with the Kerr predictions. We develop such a description for polar observers in a radial class of stationary, axisymmetric spacetimes with separable null geodesics. The spacetime dependence is organized through natural optical combinations selected by the null dynamics and a Kerr-relative representation suited to weak deviations from Kerr. We derive compact exact expressions for the polar critical radius, Lyapunov exponent, time delay, and rotation parameter, together with general first-order formulas that can be applied once the deformation functions of a specific metric are supplied. The weak-deviation analysis shows that the combined polar observables probe only a finite set of local deformation values and radial derivatives at the critical orbit, rather than the full radial profiles.
ER -