Three-dimensional wave optics for weak-field lensing of gravitational waves
4 affiliations
- 1Abdus Salam Centre for Theoretical Physics , Imperial College, London, SW7 2AZ ,
- 2School of Physics & Astronomy, University of Southampton , Highfield, Southampton, SO17 1BJ ,
- 3Imperial College Imperial Centre for Inference and Cosmology (ICIC), Department of Physics, , London SW7 2AZ ,
- 4University College London Department of Physics and Astronomy, , Gower Street, London WC1E 6BT ,
Abstract
We develop a perturbative Green’s function approach to gravitational lensing by weak gravitational potentials that need not be localized on a thin lens plane and that applies in both the wave optics and geometric optics regimes. We recast position-space integrals as Fourier, or momentum-space, integrals that appear in scattering amplitude calculations. The method gives the Born approximation directly in three dimensions and can be systematically extended to post-Born orders. For a Schwarzschild lens, we compute the leading Born term and new post-Born contributions arising from the order 𝒪(G2) correction to the potential, keeping finite-distance corrections beyond the usual paraxial expansion. We show that these general-relativistic corrections are controlled by the parameter GMω b/χeff in the small-angle regime, and are therefore negligible for standard weak-lensing configurations but become relevant in more extreme geometries (such as hierarchical triples with very small source–lens separations). We also discuss higher-order Newtonian corrections, their infrared sensitivity for a long-range potential, and the regulated form of the Newtonian potential given by the Yukawa potential. Finally, we formulate the corresponding calculation in an FLRW background, identifying the leading flat-space limit and estimating the size of curvature-induced corrections including tails. This method clarifies the regime of validity of the Born, large-distance, and paraxial approximations in gravitational-wave lensing and provides a framework for treating generic lensing potentials.
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BibTeX
@article{gonzalez2026threedimensional,
title = {{Three-dimensional wave optics for weak-field lensing of gravitational waves}},
author = {Mariana Carrillo Gonzalez and Alan Heavens and Lorne Whiteway},
journal = {Monthly Notices of the Royal Astronomical Society},
year = {2026},
month = nov,
doi = {10.1093/mnras/stag2114},
url = {https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stag2114/9013650},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Three-dimensional wave optics for weak-field lensing of gravitational waves
AU - Mariana Carrillo Gonzalez
AU - Alan Heavens
AU - Lorne Whiteway
PY - 2026
DA - 2026/11/05
JO - Monthly Notices of the Royal Astronomical Society
DO - 10.1093/mnras/stag2114
UR - https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stag2114/9013650
AB - We develop a perturbative Green’s function approach to gravitational lensing by weak gravitational potentials that need not be localized on a thin lens plane and that applies in both the wave optics and geometric optics regimes. We recast position-space integrals as Fourier, or momentum-space, integrals that appear in scattering amplitude calculations. The method gives the Born approximation directly in three dimensions and can be systematically extended to post-Born orders. For a Schwarzschild lens, we compute the leading Born term and new post-Born contributions arising from the order 𝒪(G^2) correction to the potential, keeping finite-distance corrections beyond the usual paraxial expansion. We show that these general-relativistic corrections are controlled by the parameter GMω b/χeff in the small-angle regime, and are therefore negligible for standard weak-lensing configurations but become relevant in more extreme geometries (such as hierarchical triples with very small source–lens separations). We also discuss higher-order Newtonian corrections, their infrared sensitivity for a long-range potential, and the regulated form of the Newtonian potential given by the Yukawa potential. Finally, we formulate the corresponding calculation in an FLRW background, identifying the leading flat-space limit and estimating the size of curvature-induced corrections including tails. This method clarifies the regime of validity of the Born, large-distance, and paraxial approximations in gravitational-wave lensing and provides a framework for treating generic lensing potentials.
SN - 0035-8711
SN - 1365-2966
ER -