{"id":"https://openalex.org/W2018347303","doi":"https://doi.org/10.1103/physrevd.48.4729","title":"Numerical analysis of black hole evaporation","display_name":"Numerical analysis of black hole evaporation","publication_year":1993,"publication_date":"1993-11-15","ids":{"openalex":"https://openalex.org/W2018347303","doi":"https://doi.org/10.1103/physrevd.48.4729","mag":"2018347303","pmid":"https://pubmed.ncbi.nlm.nih.gov/10016127"},"language":"en","primary_location":{"id":"doi:10.1103/physrevd.48.4729","doi":"https://doi.org/10.1103/physrevd.48.4729","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevd.48.4729","pdf_url":null,"source":{"id":"https://openalex.org/S4210190737","display_name":"Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields","issn_l":"0556-2821","issn":["0556-2821","1089-4918","1538-4500","1550-2368","1550-7998"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review D","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/hep-th/9304148","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001538936","display_name":"Tsvi Piran","orcid":"https://orcid.org/0000-0002-7964-5420","observed_orcids":["https://orcid.org/0000-0002-7964-5420"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I4210124175","display_name":"Center for Astrophysics Harvard & Smithsonian","ror":"https://ror.org/03c3r2d17","country_code":"US","type":"education","lineage":["https://openalex.org/I103187081","https://openalex.org/I136199984","https://openalex.org/I4210124175"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tsvi Piran","raw_affiliation_strings":["Center for Astrophysics, Harvard University, Cambridge, Massachusetts 02138"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Astrophysics, Harvard University, Cambridge, Massachusetts 02138","institution_ids":["https://openalex.org/I136199984","https://openalex.org/I4210124175"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035107940","display_name":"Andrew Strominger","orcid":"https://orcid.org/0000-0002-1332-4122","observed_orcids":["https://orcid.org/0000-0002-1332-4122"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]},{"id":"https://openalex.org/I4210124175","display_name":"Center for Astrophysics Harvard & Smithsonian","ror":"https://ror.org/03c3r2d17","country_code":"US","type":"education","lineage":["https://openalex.org/I103187081","https://openalex.org/I136199984","https://openalex.org/I4210124175"]},{"id":"https://openalex.org/I4405259940","display_name":"Kavli Institute for Theoretical Physics","ror":"https://ror.org/02yt0vw44","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I154570441","https://openalex.org/I4405259940"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Strominger","raw_affiliation_strings":["Center for Astrophysics, Harvard University, Cambridge, Massachusetts 02138","Institute for Theoretical Physics and Department of Physics, University of California, Santa Barbara, California 93106-4030"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Astrophysics, Harvard University, Cambridge, Massachusetts 02138","institution_ids":["https://openalex.org/I136199984","https://openalex.org/I4210124175"]},{"raw_affiliation_string":"Institute for Theoretical Physics and Department of Physics, University of California, Santa Barbara, California 93106-4030","institution_ids":["https://openalex.org/I154570441","https://openalex.org/I4405259940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8259,"has_fulltext":true,"cited_by_count":68,"citation_normalized_percentile":{"value":0.96262373,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"48","issue":"10","first_page":"4729","last_page":"4734"},"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/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"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","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/black-hole-evaporation","display_name":"black hole evaporation","score":0.9990000128746033},{"id":"https://openalex.org/keywords/dilaton-gravity","display_name":"dilaton gravity","score":0.7910000085830688},{"id":"https://openalex.org/keywords/two-dimensional-dilaton-gravity","display_name":"two-dimensional dilaton gravity","score":0.8149999976158142},{"id":"https://openalex.org/keywords/large-n-limit","display_name":"large N limit","score":0.6639999747276306},{"id":"https://openalex.org/keywords/naked-singularities","display_name":"naked singularities","score":0.8090000152587891},{"id":"https://openalex.org/keywords/boundary-conditions","display_name":"boundary conditions","score":0.6899999976158142},{"id":"https://openalex.org/keywords/extremal-black-holes","display_name":"extremal black holes","score":0.7179999947547913},{"id":"https://openalex.org/keywords/black-hole-formation","display_name":"black hole formation","score":0.5910000205039978}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7084667086601257},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.6724461913108826},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6351994276046753},{"id":"https://openalex.org/C61441594","wikidata":"https://www.wikidata.org/wiki/Q132814","display_name":"Evaporation","level":2,"score":0.5605329275131226},{"id":"https://openalex.org/C8105449","wikidata":"https://www.wikidata.org/wiki/Q285949","display_name":"Naked singularity","level":3,"score":0.4713315963745117},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.4712821841239929},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.46912074089050293},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.34955355525016785},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3330334424972534},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19430837035179138},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13004031777381897},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12939253449440002},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.11913710832595825},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.08000853657722473},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C89305328","wikidata":"https://www.wikidata.org/wiki/Q1755411","display_name":"Link-state routing protocol","level":4,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C104954878","wikidata":"https://www.wikidata.org/wiki/Q1648707","display_name":"Routing protocol","level":3,"score":0.0},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1103/physrevd.48.4729","doi":"https://doi.org/10.1103/physrevd.48.4729","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevd.48.4729","pdf_url":null,"source":{"id":"https://openalex.org/S4210190737","display_name":"Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields","issn_l":"0556-2821","issn":["0556-2821","1089-4918","1538-4500","1550-2368","1550-7998"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review D","raw_type":"journal-article"},{"id":"pmid:10016127","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/10016127","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. D, Particles and fields","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:hep-th/9304148","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/hep-th/9304148","pdf_url":"https://arxiv.org/pdf/hep-th/9304148","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":"pmh:oai:cds.cern.ch:250041","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/250041","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"doi:10.48550/arxiv.hep-th/9304148","doi":"https://doi.org/10.48550/arxiv.hep-th/9304148","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.hep-th/9304148","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":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:hep-th/9304148","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/hep-th/9304148","pdf_url":"https://arxiv.org/pdf/hep-th/9304148","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/G1796279563","display_name":null,"funder_award_id":"PHY89-04035","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G4426844816","display_name":"HIGH ENERGY USER GROUP","funder_award_id":"FG0391ER40618","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320310042","display_name":"Aspen Center for Physics","ror":"https://ror.org/05gqcbq50"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2018347303.pdf","grobid_xml":"https://content.openalex.org/works/W2018347303.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1581904054","https://openalex.org/W1972515809","https://openalex.org/W1987211198","https://openalex.org/W1998624867","https://openalex.org/W2007698550","https://openalex.org/W2008904933","https://openalex.org/W2027753262","https://openalex.org/W2040672473","https://openalex.org/W2047185722","https://openalex.org/W2055829555","https://openalex.org/W2091534981","https://openalex.org/W2134897257","https://openalex.org/W2148986778","https://openalex.org/W2156932589","https://openalex.org/W2962885739","https://openalex.org/W3105425914"],"related_works":["https://openalex.org/W2027753262","https://openalex.org/W4410612434","https://openalex.org/W7095425147","https://openalex.org/W2040504012","https://openalex.org/W2081481773","https://openalex.org/W4402270347","https://openalex.org/W4382797541","https://openalex.org/W2055829555","https://openalex.org/W3013765638","https://openalex.org/W2022985187"],"abstract_inverted_index":{"Black":[0],"hole":[1],"formation":[2],"and/or":[3],"evaporation":[4,73],"in":[5,12],"two-dimensional":[6],"dilaton":[7],"gravity":[8],"can":[9],"be":[10,82],"described,":[11],"the":[13,16,65,68,72,89,92,99],"limit":[14],"where":[15],"number":[17],"$N$":[18],"of":[19,27,102],"matter":[20],"fields":[21],"becomes":[22],"large,":[23],"by":[24,105],"a":[25,53],"set":[26],"second-order":[28],"partial":[29],"differential":[30],"equations.":[31],"In":[32],"this":[33,80],"paper":[34],"we":[35],"solve":[36],"these":[37],"equations":[38],"numerically.":[39],"It":[40,76],"is":[41,61,77],"shown":[42],"that,":[43],"contrary":[44],"to":[45,63,87,91,98],"some":[46],"previous":[47],"suggestions,":[48],"black":[49,110],"holes":[50],"evaporate":[51],"completely":[52],"finite":[54],"time":[55],"after":[56],"formation.":[57],"A":[58],"boundary":[59],"condition":[60],"required":[62],"evolve":[64],"system":[66,90],"beyond":[67],"naked":[69],"singularity":[70],"at":[71],"end":[74],"point.":[75],"argued":[78],"that":[79],"may":[81],"naturally":[83],"chosen":[84],"so":[85],"as":[86],"restore":[88],"vacuum.":[93],"The":[94],"analysis":[95],"also":[96],"applies":[97],"low-energy":[100],"scattering":[101],"$S$-wave":[103],"fermions":[104],"four-dimensional":[106],"extremal,":[107],"magnetic,":[108],"dilatonic":[109],"holes.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}