{
  "abstract": "The Bekenstein-Hawking law fixes the total entropy of a horizon. Membrane, holographic, and entropic-force pictures go further and follow the entropy of individual horizon elements as a configuration changes. We show that this step needs structure that the horizon geometry does not supply. Along a family of horizons labeled by $λ$, a relabeling of horizon points by a tangential field $v^A$ shifts the temperature-weighted entropy variation $\\int T\\partial_λ(dS)$ exactly by $-\\int v^AD_AT dS$, so the horizon data determine it only when the temperature is uniform. We test this on two black holes in exact Brill-Lindquist data. At fixed physical masses each horizon area is independent of the separation through five relative orders; the low-order equilibrium force reported earlier comes from holding the bare parameters fixed instead. Weighting the redistribution of area by the nonuniform Noether-charge temperature gives a candidate repulsion equal to $(ν/8)(GM/r_{12})^3$ times the Newtonian attraction, for total mass $M$, symmetric mass ratio $ν$, and coordinate separation $r_{12}$. As a static interaction it would shift the third post-Newtonian coefficient of the circular-orbit binding energy by $5ν/48$, in conflict with general relativity. The identity resolves the conflict. Through fourth post-Newtonian order the candidate lies entirely in the dipole of the area distribution, which the uniform part of the companion's field generates as a Möbius map of the labels, and which vanishes in the area-balanced conformal frame, where the functional begins at fifth order with a coefficient that a further relabeling can still change. The marginally trapped tube of the data and the tidally deformed horizon of a post-Newtonian binary, both of which do supply an identification, transport no dipole at the order the candidate requires.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31690",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhi-Wei Wang"
    },
    {
      "name": "Samuel L. Braunstein"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6x7gpf3qewtk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31690",
  "fulltext_url": null,
  "id": "f6x7gpf3qewtk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31690",
  "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"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223657769",
  "pdf_url": "https://arxiv.org/pdf/2610.31690",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6x7gpf3qewtk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.31690",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31690"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Horizon entropy does not by itself determine a force between black holes",
  "title_text": "Horizon entropy does not by itself determine a force between black holes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:15Z",
  "url": "https://research.draconitic.com/paper/f6x7gpf3qewtk",
  "venue": "arXiv",
  "versions": []
}