{
  "abstract": "A massless particle on the circular null geodesic of a Schwarzschild or Kerr black hole radiates gravitational waves at all multipoles $\\ell$ with a power that falls off only as $1/\\ell$, so that the total instantaneous power is logarithmically divergent. We derive this result analytically from the Zerilli--Regge--Wheeler and Teukolsky equations with a null stress-energy tensor as source, and find that both the power radiated to infinity and the power absorbed by the horizon approach $\\dot{E}_\\ell\\to g(a) κE^2/(M^2\\ell)$, where $E$ is the energy of the particle, $M$ the mass of the black hole and $a$ its spin, with $κ=0.063653$ and a spin factor $g(a)$, for which we obtain, for any spin, the closed form $g=27M^2(r_0-M)/[r_0^2(r_0+3M)]$ in terms of the radius $r_0$ of the Kerr light ring. The $1/\\ell$ behavior has two causes: the near-resonance of the photon with the quasinormal modes, which prevents any exponential suppression at large $\\ell$, and a cancellation in the source that is specific to massless particles, which reduces the power per multipole by a factor $\\ell^2$ with respect to a generic source. At leading order half of the radiation falls into the black hole, and we compute the first correction to this equal split in the non-spinning case. The same analysis describes massive particles on orbits close to the light ring, where the mass turns the $1/\\ell$ law into an exponential cut-off. We recover the dominant, even-parity term of the geodesic synchrotron radiation formulae for massive particles of Breuer, Ruffini, Tiomno and Vishveshwara (1973), but we find that their odd-parity term is too small by a factor of four. All results are checked against numerical solutions, up to $\\ell=12800$ in Schwarzschild and $\\ell=800$ in Kerr.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12082",
  "author_total": 1,
  "authors": [
    {
      "name": "Enrico Barausse"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cwc2vpddacp6v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12082",
  "fulltext_url": null,
  "id": "cwc2vpddacp6v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12082",
  "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"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7221117465",
  "pdf_url": "https://arxiv.org/pdf/2610.12082",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cwc2vpddacp6v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12082",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12082"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Gravitational radiation from a photon on the light ring: multipole fluxes and the logarithmic divergence",
  "title_text": "Gravitational radiation from a photon on the light ring: multipole fluxes and the logarithmic divergence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/cwc2vpddacp6v",
  "venue": "arXiv",
  "versions": []
}