Strong-field gravitational-wave lensing in the Kerr background
Phys. Rev. D 113, 084056 – Published 27 April, 2026
DOI: https://doi.org/10.1103/9bxg-sqn5
Abstract
Gravitational lensing of gravitational waves (GWs) can encode valuable information about the properties of the intervening lens, but most existing studies remain restricted to the small-deflection, weak-field regime. To bridge this crucial gap, this work presents the first systematic analysis of strong-field, wave-optical GW lensing by a Kerr black hole (BH), extending recent results obtained in [Phys. Rev. D 112, 064009 (2025)] for nonrotating lens to the astrophysically more relevant case of spinning-lens. Using the Mano-Suzuki-Takasugi formalism, we define and compute the strong-field scattering factor (SFSF) and show that the spin produces characteristic modifications to the lensed waveform, and high-frequency incident radiation is not strongly absorbed by the BH lens, contrary to earlier claims in the abovementioned paper. We further derive an explicit expression for the observed waveform for the general source-lens-observer configuration, showcasing the distortions produced by the scattering and quantifying their departure from the Schwarzschild case. Specializing to on-axis scattering, a mismatch analysis for a GW150914-like source lensed by a Kerr BH of mass situated away from the source reveals percentage-level deviations from the direct (unscattered) wave at scattering angles near radians, across a range of lens spin values. The mismatch generally decreases as the scattering angle increases, but this behavior can change substantially when polarization mixing induced by scattering becomes significant. In such cases, components that are absent or suppressed in the direct signal may become appreciable once scattering effects are taken into account. For a fixed scattering angle, however, the mismatch shows only a weak dependence on the BH spin in the case of on-axis scattering, which may improve for more general off-axis considerations. The framework developed here offers a unified treatment of strong-field GW scattering in Kerr spacetime and provides tools for interpreting future high-precision observations of compact-object lenses in the wave-optics regime.
