{
  "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 $\\mathcal {O}(G^2)$ 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.",
  "abstract_shown": true,
  "affiliations": [
    "Abdus Salam Centre for Theoretical Physics , Imperial College, London, SW7 2AZ ,",
    "School of Physics & Astronomy, University of Southampton , Highfield, Southampton, SO17 1BJ ,",
    "Imperial College Imperial Centre for Inference and Cosmology (ICIC), Department of Physics, , London SW7 2AZ ,",
    "University College London Department of Physics and Astronomy, , Gower Street, London WC1E 6BT ,"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Mariana Carrillo Gonzalez"
    },
    {
      "affs": [
        2
      ],
      "name": "Alan Heavens"
    },
    {
      "affs": [
        3
      ],
      "name": "Lorne Whiteway"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahxmpecx2y78m.bib",
  "cited_by": 0,
  "doi": "10.1093/mnras/stag2114",
  "fulltext_url": null,
  "id": "ahxmpecx2y78m",
  "issns": [
    "0035-8711",
    "1365-2966"
  ],
  "landing_url": "https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stag2114/9013650",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://academic.oup.com/mnras/advance-article-pdf/doi/10.1093/mnras/stag2114/73135196/stag2114.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": "Oxford University Press (OUP)",
  "ris": "https://research.draconitic.com/paper/ahxmpecx2y78m.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T00:21:01Z",
      "native_id": "10.1093/mnras/stag2114",
      "source": "crossref",
      "url": "https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stag2114/9013650"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "journal-openalex:3103|Stellar, planetary, and galactic studies",
      "subfield": "stellar"
    }
  ],
  "title": "Three-dimensional wave optics for weak-field lensing of gravitational waves",
  "title_text": "Three-dimensional wave optics for weak-field lensing of gravitational waves",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T00:21:01Z",
  "url": "https://research.draconitic.com/paper/ahxmpecx2y78m",
  "venue": "Monthly Notices of the Royal Astronomical Society",
  "versions": []
}