{
  "abstract": "We investigate the low-frequency behavior of the amplification factor in gravitational lensing and explore how it encodes information about the density profile of the lensing object. We derive the low-frequency expansion of the amplification factor under the Born approximation for a broad class of projected density profiles. For spherically symmetric profiles that decay faster than any power law at large distances, we derive a systematic expansion of the amplification factor in powers of frequency, with the logarithmic dependence appearing only in the leading term, and show that each expansion coefficient is determined by a finite set of moments of the density profile. We then extend the analysis to profiles with power-law tails and demonstrate that such profiles induce additional non-analytic frequency dependences, including fractional powers and logarithmic terms, which directly reflect the asymptotic behavior of the density distribution. Furthermore, we investigate the effects of non-sphericity and show that contributions from the quadrupole moment appear only as higher-order corrections relative to the spherically symmetric component in the low-frequency regime. Finally, we investigate the validity of the Born approximation in the low-frequency expansion. We derive a criterion for the maximum order of the low-frequency expansion up to which the Born approximation remains dominant over the post-Born corrections.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09704",
  "author_total": 2,
  "authors": [
    {
      "name": "So Tanaka"
    },
    {
      "name": "Teruaki Suyama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0d6148dpxzw4k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09704",
  "fulltext_url": null,
  "id": "0d6148dpxzw4k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09704",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7212186777",
  "pdf_url": "https://arxiv.org/pdf/2609.09704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0d6148dpxzw4k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.09704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09704"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "A universal connection between lens density profiles and low-frequency wave optics in gravitational-wave lensing",
  "title_text": "A universal connection between lens density profiles and low-frequency wave optics in gravitational-wave lensing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:03Z",
  "url": "https://research.draconitic.com/paper/0d6148dpxzw4k",
  "venue": "arXiv",
  "versions": []
}