{"id":"https://openalex.org/W7214092691","doi":"https://doi.org/10.48550/arxiv.2609.25218","title":"The BTZ black hole, the Third Law and gravitational collapse","display_name":"The BTZ black hole, the Third Law and gravitational collapse","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214092691","doi":"https://doi.org/10.48550/arxiv.2609.25218"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25218","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25218","pdf_url":"https://arxiv.org/pdf/2609.25218","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.25218","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120282600","display_name":"Aidan M. McSharry","orcid":"https://orcid.org/0009-0003-8686-3711","observed_orcids":["https://orcid.org/0009-0003-8686-3711"]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"McSharry, Aidan M.","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics , University of Cambridge Wilberforce Road , Cambridge CB3 0WA , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics , University of Cambridge Wilberforce Road , Cambridge CB3 0WA , United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086052031","display_name":"Harvey S. Reall","orcid":"https://orcid.org/0000-0003-1363-6369","observed_orcids":["https://orcid.org/0000-0003-1363-6369"]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Reall, Harvey S.","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics , University of Cambridge Wilberforce Road , Cambridge CB3 0WA , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics , University of Cambridge Wilberforce Road , Cambridge CB3 0WA , United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061177898","display_name":"Jorge E. Santos","orcid":"https://orcid.org/0000-0002-4199-4190","observed_orcids":["https://orcid.org/0000-0002-4199-4190"]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Santos, Jorge E.","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics , University of Cambridge Wilberforce Road , Cambridge CB3 0WA , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics , University of Cambridge Wilberforce Road , Cambridge CB3 0WA , United Kingdom","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10744","display_name":"Astrophysical Phenomena and Observations","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/btz-black-hole","display_name":"BTZ black hole","score":0.9959999918937683},{"id":"https://openalex.org/keywords/gravitational-collapse","display_name":"gravitational collapse","score":0.8820000290870667},{"id":"https://openalex.org/keywords/trapped-surfaces","display_name":"trapped surfaces","score":0.6100000143051147},{"id":"https://openalex.org/keywords/dominant-energy-condition","display_name":"dominant energy condition","score":0.8579999804496765},{"id":"https://openalex.org/keywords/quasilocal-energy","display_name":"quasilocal energy","score":0.8209999799728394},{"id":"https://openalex.org/keywords/massless-scalar-field","display_name":"massless scalar field","score":0.8700000047683716},{"id":"https://openalex.org/keywords/neveu-schwarz-sector","display_name":"Neveu-Schwarz sector","score":0.8769999742507935},{"id":"https://openalex.org/keywords/ramond-sector","display_name":"Ramond sector","score":0.9929999709129333},{"id":"https://openalex.org/keywords/supersymmetry","display_name":"supersymmetry","score":0.7490000128746033},{"id":"https://openalex.org/keywords/three-dimensional-gravity","display_name":"three-dimensional gravity","score":0.7269999980926514},{"id":"https://openalex.org/keywords/event-horizon","display_name":"event horizon","score":0.8309999704360962}],"concepts":[{"id":"https://openalex.org/C36796876","wikidata":"https://www.wikidata.org/wiki/Q4836741","display_name":"BTZ black hole","level":5,"score":0.939300000667572},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7269999980926514},{"id":"https://openalex.org/C148292158","wikidata":"https://www.wikidata.org/wiki/Q181741","display_name":"Event horizon","level":3,"score":0.6935999989509583},{"id":"https://openalex.org/C118396296","wikidata":"https://www.wikidata.org/wiki/Q329273","display_name":"Gravitational collapse","level":2,"score":0.5670999884605408},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.501800000667572},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.4814000129699707},{"id":"https://openalex.org/C54937798","wikidata":"https://www.wikidata.org/wiki/Q2024141","display_name":"Massless particle","level":2,"score":0.4731999933719635},{"id":"https://openalex.org/C149643647","wikidata":"https://www.wikidata.org/wiki/Q986455","display_name":"Energy condition","level":3,"score":0.4494999945163727},{"id":"https://openalex.org/C155675718","wikidata":"https://www.wikidata.org/wiki/Q161254","display_name":"Angular momentum","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3952000141143799},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.38850000500679016},{"id":"https://openalex.org/C82422596","wikidata":"https://www.wikidata.org/wiki/Q1094364","display_name":"Rotating black hole","level":3,"score":0.38679999113082886},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.385699987411499},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C104062141","wikidata":"https://www.wikidata.org/wiki/Q2601295","display_name":"Extremal black hole","level":3,"score":0.32760000228881836},{"id":"https://openalex.org/C2991699761","wikidata":"https://www.wikidata.org/wiki/Q7785067","display_name":"Third law","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.30550000071525574},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C22492302","wikidata":"https://www.wikidata.org/wiki/Q2297853","display_name":"Gravitational energy","level":3,"score":0.2874999940395355},{"id":"https://openalex.org/C14257148","wikidata":"https://www.wikidata.org/wiki/Q558066","display_name":"Gravitational field","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C17777063","wikidata":"https://www.wikidata.org/wiki/Q4780925","display_name":"Apparent horizon","level":4,"score":0.2752000093460083},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.26969999074935913},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25218","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25218","pdf_url":"https://arxiv.org/pdf/2609.25218","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.25218","doi":"https://doi.org/10.48550/arxiv.2609.25218","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25218","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.25218","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25218","pdf_url":"https://arxiv.org/pdf/2609.25218","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4786312554","display_name":"Quantum Fields, Quantum Gravity and Quantum Particles","funder_award_id":"ST/X000664/1","funder_id":"https://openalex.org/F4320334632","funder_display_name":"Science and Technology Facilities Council"}],"funders":[{"id":"https://openalex.org/F4320334632","display_name":"Science and Technology Facilities Council","ror":"https://ror.org/057g20z61"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214092691.pdf","grobid_xml":"https://content.openalex.org/works/W7214092691.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1763748250","https://openalex.org/W2055760067","https://openalex.org/W2060083150","https://openalex.org/W2153274301","https://openalex.org/W2502854791","https://openalex.org/W2599867241"],"related_works":["https://openalex.org/W4415965622","https://openalex.org/W2912504417","https://openalex.org/W4405800896","https://openalex.org/W7100964371","https://openalex.org/W4406870571","https://openalex.org/W7214219997","https://openalex.org/W7159615842","https://openalex.org/W7152620233","https://openalex.org/W7204188032","https://openalex.org/W2106374997"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,30,46,84,95,141],"a":[3,34,43,69,81,99],"Third":[4],"Law":[5],"of":[6,58,98,108],"black":[7,14,44,112],"hole":[8,15,45,113],"mechanics":[9],"holds":[10],"for":[11,55],"the":[12,23,52,88,106,128,137,151],"BTZ":[13,50,90,111,133,146],"in":[16,39,105,114,127,136,147],"3d":[17],"gravity":[18],"coupled":[19],"to":[20,42,79,144],"matter":[21],"obeying":[22],"dominant":[24],"energy":[25,71],"condition.":[26],"This":[27],"law":[28],"states":[29],"initial":[31],"data":[32],"containing":[33],"trapped":[35],"surface":[36],"cannot":[37],"evolve":[38],"finite":[40,115],"time":[41,149],"coincides":[47],"with":[48],"extremal":[49,89,110,132,145],"on":[51],"event":[53,152],"horizon,":[54],"any":[56],"choice":[57],"boundary":[59],"conditions":[60],"at":[61],"infinity.":[62],"The":[63,117],"result":[64,104],"is":[65,85,134],"proved":[66],"by":[67,87],"defining":[68],"quasilocal":[70],"and":[72,75],"angular":[73],"momentum":[74],"using":[76],"spinorial":[77],"methods":[78],"establish":[80],"BPS":[82],"inequality":[83],"saturated":[86],"solution.":[91],"Nevertheless,":[92],"we":[93],"show":[94],"gravitational":[96,124],"collapse":[97,125],"massless":[100],"scalar":[101],"field":[102],"can":[103],"formation":[107],"an":[109],"time.":[116],"difference":[118],"between":[119],"these":[120],"results":[121],"arises":[122],"because":[123],"occurs":[126],"Neveu-Schwarz":[129],"sector,":[130],"whereas":[131],"supersymmetric":[135],"Ramond":[138],"sector.":[139],"Solutions":[140],"settle":[142],"down":[143],"infinite":[148],"along":[150],"horizon":[153],"are":[154],"also":[155],"discussed.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}
