Gravitational lensing of gravitational waves by a Kerr black hole
Abstract
We simulate the gravitational lensing of gravitational waves (GWs) by a Kerr black hole using a (1+1)-dimensional time-domain mode-sum approach. To enable efficient explicit time evolution, we implement a localized hyperboloidal foliation combined with a static field redefinition, ensuring bounded characteristic speeds across an extended, uniform tortoise-coordinate grid. Incident GW initial data are constructed by projecting a plane-wave Weyl tensor onto the Kinnersley tetrad. Through local spin-dyad rotations and Wigner D-matrix transformations, our framework accommodates both idealized wave packets and realistic binary coalescence signals at arbitrary incidence and polarization angles. To accurately resolve the lensed waveforms, we evolve over $68,000$ coupled (j,m) modes. Our results reveal that a Kerr black hole acts as a diffraction-limited thick lens, focusing GWs into a forward beam. For idealized wave packets, the primary prompt pulse exhibits a spin-independent transverse Gaussian profile, whereas the subsequent lensing coda is sensitive to the black hole's spin. For binary coalescence signals, strong-field lensing substantially modifies the post-merger ringdown. However, the lensed inspiral and merger phases in Kerr and Schwarzschild backgrounds are virtually identical, yielding waveform mismatches below 2.2×10−5 across various inclinations and polarizations. These findings demonstrate that non-spinning Schwarzschild models provide an accurate and computationally economical surrogate to search for strong-field lensing signatures with current ground-based detectors.
Related
- Observational Signatures of Kerr Black Hole Lensing
- Observational signatures of Kerr black hole lensing
- Gravitational waves from inclined orbits around Kerr black holes
- Gravitational Lensing Signatures of a Black Hole in Mimetic Euler-Heisenberg theory
- Neutron Star--Primordial Black Hole Binaries: Dynamical Tides, Resonance Locking, and Gravitational Waves
BibTeX
@misc{he2026gravitational,
title = {{Gravitational lensing of gravitational waves by a Kerr black hole}},
author = {Jian-hua He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39181},
eprint = {2610.39181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39181},
}
RIS
TY - UNPB
TI - Gravitational lensing of gravitational waves by a Kerr black hole
AU - Jian-hua He
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39181
UR - https://arxiv.org/abs/2610.39181
AB - We simulate the gravitational lensing of gravitational waves (GWs) by a Kerr black hole using a (1+1)-dimensional time-domain mode-sum approach. To enable efficient explicit time evolution, we implement a localized hyperboloidal foliation combined with a static field redefinition, ensuring bounded characteristic speeds across an extended, uniform tortoise-coordinate grid. Incident GW initial data are constructed by projecting a plane-wave Weyl tensor onto the Kinnersley tetrad. Through local spin-dyad rotations and Wigner D-matrix transformations, our framework accommodates both idealized wave packets and realistic binary coalescence signals at arbitrary incidence and polarization angles. To accurately resolve the lensed waveforms, we evolve over $68,000$ coupled (j,m) modes. Our results reveal that a Kerr black hole acts as a diffraction-limited thick lens, focusing GWs into a forward beam. For idealized wave packets, the primary prompt pulse exhibits a spin-independent transverse Gaussian profile, whereas the subsequent lensing coda is sensitive to the black hole's spin. For binary coalescence signals, strong-field lensing substantially modifies the post-merger ringdown. However, the lensed inspiral and merger phases in Kerr and Schwarzschild backgrounds are virtually identical, yielding waveform mismatches below 2.2×10^−5 across various inclinations and polarizations. These findings demonstrate that non-spinning Schwarzschild models provide an accurate and computationally economical surrogate to search for strong-field lensing signatures with current ground-based detectors.
ER -