Gravitational Lensing of Gravitational Waves: Spin-wave Optics through Black Hole Scattering
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914225196105728 |
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| author | Li, Zhao Hou, Shaoqi Zhao, Wen |
| author_facet | Li, Zhao Hou, Shaoqi Zhao, Wen |
| contents | Gravitational-wave (GW) scattering in strong gravitational fields is a central problem in GW lensing. Yet, conventional treatments based on asymptotic expansions suffer from divergences and become unreliable near the optical axis. In this work, we present a rigorous calculation of GW scattering by a Schwarzschild black hole (BH) within the BH perturbation theory. By placing the observer at a finite distance and abandoning the asymptotic expansion of radial wave functions, we obtain a well-convergent partial-wave description without invoking any regularization scheme, thereby naturally resolving the divergences of the partial-wave series and the Poisson spot. We numerically computed the scattered GW waveforms by reconstructing the physical $+$ and $\times$ polarizations from the master variables, revealing the formation of the Poisson spot and pronounced wavefront distortions. A systematic comparison with conventional asymptotic approaches shows that they reproduce only qualitative features at large scattering angles and fail in the forward-scattering region. We further compare the frequency-domain transmission factors derived from the scattering formalism with those obtained from the Kirchhoff diffraction integral, finding significant discrepancies at high frequencies due to the latter's neglect of long-range gravitational effects and polarization evolution. Our results establish a stable and physically transparent framework for GW scattering in strong-field regimes and provide a solid foundation for accurate modeling of GW lensing beyond standard approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gravitational Lensing of Gravitational Waves: Spin-wave Optics through Black Hole Scattering Li, Zhao Hou, Shaoqi Zhao, Wen General Relativity and Quantum Cosmology Gravitational-wave (GW) scattering in strong gravitational fields is a central problem in GW lensing. Yet, conventional treatments based on asymptotic expansions suffer from divergences and become unreliable near the optical axis. In this work, we present a rigorous calculation of GW scattering by a Schwarzschild black hole (BH) within the BH perturbation theory. By placing the observer at a finite distance and abandoning the asymptotic expansion of radial wave functions, we obtain a well-convergent partial-wave description without invoking any regularization scheme, thereby naturally resolving the divergences of the partial-wave series and the Poisson spot. We numerically computed the scattered GW waveforms by reconstructing the physical $+$ and $\times$ polarizations from the master variables, revealing the formation of the Poisson spot and pronounced wavefront distortions. A systematic comparison with conventional asymptotic approaches shows that they reproduce only qualitative features at large scattering angles and fail in the forward-scattering region. We further compare the frequency-domain transmission factors derived from the scattering formalism with those obtained from the Kirchhoff diffraction integral, finding significant discrepancies at high frequencies due to the latter's neglect of long-range gravitational effects and polarization evolution. Our results establish a stable and physically transparent framework for GW scattering in strong-field regimes and provide a solid foundation for accurate modeling of GW lensing beyond standard approximations. |
| title | Gravitational Lensing of Gravitational Waves: Spin-wave Optics through Black Hole Scattering |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.23933 |