{
  "abstract": "We develop an inverse lensing formalism for reconstructing the metric function of a static, spherically symmetric spacetime directly from the gravitational deflection angle of light. By formulating the inverse problem through an Abel transformation, we derive an integro-differential relation connecting the observable deflection profile to the underlying spacetime geometry. As a consistency check, we consider the case of vanishing deflection, \\(α(b)=0\\), and recover \\(A(r)=1\\), corresponding to flat Minkowski spacetime. We then apply the formalism to the gravitational deflection of light by the Sun using the observationally motivated leading-order expression $α(b)=\\frac{2(1+γ)GM_{\\odot}}{c^{2}b}.$The resulting metric function is shown to recover the Schwarzschild form in the weak-field limit \\(r\\gg M\\). We further consider the higher-order correction to the solar deflection angle and reconstruct the corresponding metric beyond the leading-order approximation. Interestingly, the \\((M/r)^2\\) term vanishes in the resulting weak-field expansion, yielding an improved approximation compared with the metric reconstructed from the leading-order deflection angle. Our results demonstrate that gravitational lensing observations can provide a direct route to reconstructing the underlying spacetime geometry without assuming a specific metric a priori. This formalism therefore, offers a novel framework for connecting observational light propagation with spacetime geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16844",
  "author_total": 2,
  "authors": [
    {
      "name": "Aniruddha Ghosh"
    },
    {
      "name": "Ujjal Debnath"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/46mad44q3fd8s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16844",
  "fulltext_url": null,
  "id": "46mad44q3fd8s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16844",
  "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",
      "gr-qc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.16844",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/46mad44q3fd8s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16844",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16844"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "An Abel-Inversion Formalism for Spacetime Metric Reconstruction from Light Deflection",
  "title_text": "An Abel-Inversion Formalism for Spacetime Metric Reconstruction from Light Deflection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/46mad44q3fd8s",
  "venue": "arXiv",
  "versions": []
}