Uniform Strong-Deflection Lensing in Near-Extremal Kerr
Abstract
Strong-deflection lensing by a subextremal Kerr black hole exhibits a logarithmic critical divergence, whereas the exactly extremal prograde problem develops stronger power-law behavior. We construct a uniform asymptotic description of the transition between these regimes for prograde equatorial null geodesics. The distinguished joint near-critical and near-extremal limit occurs when the impact-parameter offset from the exact critical value is of order Mκ, where κ=√(1−a2/M2). In this limit, the Kerr radial potential reduces to a quadratic normal form, yielding an analytic crossover function that connects the subextremal logarithmic and extremal power-law regimes. We derive a matched next-to-leading-order correction and validate it against high-precision integrations of the exact Kerr geodesic equations, finding improvement for all 55 trajectories tested. The same asymptotic structure yields a higher-order image-branch law interpolating between algebraic and exponential accumulation, with crossover order scaling as κ−1. We also derive and numerically validate the corresponding image-branch coordinate-time delay law, whose high-order extremal-like limit approaches the horizon-period spacing 4πM.
Related
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- Kerr-Degenerate Shadows and Distinct Strong-Deflection Lensing in Rotating Hayward-like and Bardeen-like Geometries
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BibTeX
@misc{chowdhury2026uniform,
title = {{Uniform Strong-Deflection Lensing in Near-Extremal Kerr}},
author = {Shakibul Chowdhury},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02900},
eprint = {2610.02900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02900},
}
RIS
TY - UNPB
TI - Uniform Strong-Deflection Lensing in Near-Extremal Kerr
AU - Shakibul Chowdhury
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02900
UR - https://arxiv.org/abs/2610.02900
AB - Strong-deflection lensing by a subextremal Kerr black hole exhibits a logarithmic critical divergence, whereas the exactly extremal prograde problem develops stronger power-law behavior. We construct a uniform asymptotic description of the transition between these regimes for prograde equatorial null geodesics. The distinguished joint near-critical and near-extremal limit occurs when the impact-parameter offset from the exact critical value is of order Mκ, where κ=√(1−a^2/M^2). In this limit, the Kerr radial potential reduces to a quadratic normal form, yielding an analytic crossover function that connects the subextremal logarithmic and extremal power-law regimes. We derive a matched next-to-leading-order correction and validate it against high-precision integrations of the exact Kerr geodesic equations, finding improvement for all 55 trajectories tested. The same asymptotic structure yields a higher-order image-branch law interpolating between algebraic and exponential accumulation, with crossover order scaling as κ^−1. We also derive and numerically validate the corresponding image-branch coordinate-time delay law, whose high-order extremal-like limit approaches the horizon-period spacing 4πM.
ER -