{
  "abstract": "We prove that a Third Law of black hole mechanics holds for the BTZ black hole in 3d gravity coupled to matter obeying the dominant energy condition. This law states that initial data containing a trapped surface cannot evolve in finite time to a black hole that coincides with extremal BTZ on the event horizon, for any choice of boundary conditions at infinity. The result is proved by defining a quasilocal energy and angular momentum and using spinorial methods to establish a BPS inequality that is saturated by the extremal BTZ solution. Nevertheless, we show that gravitational collapse of a massless scalar field can result in the formation of an extremal BTZ black hole in finite time. The difference between these results arises because gravitational collapse occurs in the Neveu-Schwarz sector, whereas extremal BTZ is supersymmetric in the Ramond sector. Solutions that settle down to extremal BTZ in infinite time along the event horizon are also discussed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25218",
  "author_total": 3,
  "authors": [
    {
      "name": "Aidan M. McSharry"
    },
    {
      "name": "Harvey S. Reall"
    },
    {
      "name": "Jorge E. Santos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cz5yatjrar3qy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25218",
  "fulltext_url": null,
  "id": "cz5yatjrar3qy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25218",
  "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": "W7214092691",
  "pdf_url": "https://arxiv.org/pdf/2609.25218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cz5yatjrar3qy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25218"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The BTZ black hole, the Third Law and gravitational collapse",
  "title_text": "The BTZ black hole, the Third Law and gravitational collapse",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/cz5yatjrar3qy",
  "venue": "arXiv",
  "versions": []
}