{
  "abstract": "We examine whether scalar eikonal quasinormal-mode data determine black-hole thermodynamics. For static, spherically symmetric, asymptotically flat, nonextremal geometries, we prove that the formal fixed-overtone expansion of a neutral, minimally coupled, massless scalar through order $L^{-N}$ depends only on the $(2N+2)$ jet of the lapse at the unstable photon sphere. For every finite $N$, real-analytic deformations can preserve this jet and the asymptotic Reissner--Nordström coefficients while changing the surface gravity and Hawking temperature. We also construct a nonanalytic $C^\\infty$ deformation that is flat at the photon sphere. This deformation preserves the complete formal eikonal series to every algebraic order but changes the horizon position, temperature, and Einstein area entropy. A nonempty charged subfamily satisfies the weak energy condition as an effective Einstein source. Together, these four results establish the new finite-jet and all-orders thermodynamic obstruction. To separate geometric information from action-dependent information, we incorporate a previously established Reissner--Nordström--MOG comparison. The mapped backgrounds have identical normalized metrics, neutral-scalar boundary-value problems, exact scalar spectra, and Hawking temperatures, yet their Wald entropies differ because their curvature couplings differ. The resulting hierarchy shows that local photon-sphere data do not determine horizon thermodynamics and that even exact action-blind scalar data do not determine gravitational entropy. Agreement of the formal eikonal expansions for the deformed metrics does not imply exact finite-$\\ell$ isospectrality. Global differences may appear beyond every algebraic order. Thermodynamic reconstruction from eikonal ringdown is therefore conditional on assumptions about the global metric and the gravitational action.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20573",
  "author_total": 2,
  "authors": [
    {
      "name": "Nikko John Leo S. Lobos"
    },
    {
      "name": "Emmanuel T. Rodulfo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crfcrwmkxwhds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20573",
  "fulltext_url": null,
  "id": "crfcrwmkxwhds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20573",
  "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",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7170442751",
  "pdf_url": "https://arxiv.org/pdf/2607.20573",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crfcrwmkxwhds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2607.20573",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20573"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Photon sphere jet equivalence and the non-uniqueness of black-hole thermodynamics",
  "title_text": "Photon sphere jet equivalence and the non-uniqueness of black-hole thermodynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/crfcrwmkxwhds",
  "venue": "arXiv",
  "versions": []
}