{
  "abstract": "The static Love numbers of black holes vanish in classical, four-dimensional, asymptotically flat General Relativity. We study how this changes for the response of near-extremal Reissner--Nordström black holes to a minimally coupled massless scalar, at energies where the Schwarzian mode of the near-horizon throat fluctuates strongly. The black hole then responds as a quantum system with a spectrum of states. Its static response is a polarizability, given by virtual transitions between them. For $\\ell=0$ the static Love number vanishes, by the shift symmetry of the scalar, but for multipoles $\\ell\\geq1$ the static Love numbers are nonzero: the finite rotational energy of the spin-$\\ell$ intermediate states spoils the cancellation responsible for the classical result. Since the throat no longer has a classical geometry from which to read off a tidal response, we define it through the retarded Green's function, and compute its full frequency dependence at leading order in $r_+ω$. Its conservative part requires renormalization: the near-horizon theory fixes the coefficient of its logarithm, and with it a dependence on the energy that no local term can remove, while its finite local terms are matching data of the four-dimensional theory. The dissipative part is finite and scheme independent. For $\\ell\\geq1$, it vanishes at low frequencies when the energy is below the rotational gap, while at the gap threshold it becomes non-analytic in frequency and produces a late-time $t^{-3/2}$ tail.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17259",
  "author_total": 4,
  "authors": [
    {
      "name": "Pablo A. Cano"
    },
    {
      "name": "Marina David"
    },
    {
      "name": "Roberto Emparan"
    },
    {
      "name": "Stefano Trezzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ydfracjkz2av.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17259",
  "fulltext_url": null,
  "id": "1ydfracjkz2av",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17259",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7221834355",
  "pdf_url": "https://arxiv.org/pdf/2610.17259",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ydfracjkz2av.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.17259",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17259"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Love at First Loop: Quantum Deformability of Near-Extremal Black Holes",
  "title_text": "Love at First Loop: Quantum Deformability of Near-Extremal Black Holes",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:17Z",
  "url": "https://research.draconitic.com/paper/1ydfracjkz2av",
  "venue": "arXiv",
  "versions": []
}