{"id":"https://openalex.org/W2071917424","doi":"https://doi.org/10.1088/0264-9381/20/15/312","title":"Quick and dirty methods for studying black-hole resonances","display_name":"Quick and dirty methods for studying black-hole resonances","publication_year":2003,"publication_date":"2003-07-16","ids":{"openalex":"https://openalex.org/W2071917424","doi":"https://doi.org/10.1088/0264-9381/20/15/312","mag":"2071917424"},"language":"en","primary_location":{"id":"doi:10.1088/0264-9381/20/15/312","doi":"https://doi.org/10.1088/0264-9381/20/15/312","is_oa":true,"landing_page_url":"https://doi.org/10.1088/0264-9381/20/15/312","pdf_url":"https://iopscience.iop.org/article/10.1088/0264-9381/20/15/312/pdf","source":{"id":"https://openalex.org/S171172751","display_name":"Classical and Quantum Gravity","issn_l":"0264-9381","issn":["0264-9381","1361-6382"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","ki-jl-1","norway-1"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Classical and Quantum Gravity","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://iopscience.iop.org/article/10.1088/0264-9381/20/15/312/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Kostas Glampedakis","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kostas Glampedakis","raw_affiliation_strings":["Department of Physics and Astronomy, Cardiff University PO Box 913, Cardiff, CF24 3YB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, Cardiff University PO Box 913, Cardiff, CF24 3YB, UK","institution_ids":["https://openalex.org/I79510175"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079852983","display_name":"Nils Andersson","orcid":"https://orcid.org/0000-0001-8550-3843","observed_orcids":["https://orcid.org/0000-0001-8550-3843"]},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Nils Andersson","raw_affiliation_strings":["Department of Mathematics, University of Southampton, Southampton SO17 1BJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Southampton, Southampton SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3325,"currency":"USD","value_usd":3325},"apc_paid":null,"fwci":2.6083,"has_fulltext":true,"cited_by_count":81,"citation_normalized_percentile":{"value":0.89757422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"20","issue":"15","first_page":"3441","last_page":"3463"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9023000001907349,"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":0.9023000001907349,"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/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.06069999933242798,"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":0.010900000110268593,"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/quasinormal-modes","display_name":"quasinormal modes","score":0.9959999918937683},{"id":"https://openalex.org/keywords/regge-poles","display_name":"Regge poles","score":1.0},{"id":"https://openalex.org/keywords/teukolsky-equation","display_name":"Teukolsky equation","score":0.8320000171661377},{"id":"https://openalex.org/keywords/s-matrix-poles","display_name":"S-matrix poles","score":0.7699999809265137},{"id":"https://openalex.org/keywords/rotating-black-holes","display_name":"rotating black holes","score":0.7910000085830688},{"id":"https://openalex.org/keywords/schwarzschild-black-hole","display_name":"Schwarzschild black hole","score":0.9779999852180481},{"id":"https://openalex.org/keywords/excitation-coefficients","display_name":"excitation coefficients","score":0.8040000200271606},{"id":"https://openalex.org/keywords/scalar-waves","display_name":"scalar waves","score":0.8899999856948853}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.9466999769210815},{"id":"https://openalex.org/C155675718","wikidata":"https://www.wikidata.org/wiki/Q161254","display_name":"Angular momentum","level":2,"score":0.6747000217437744},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6065000295639038},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.5774999856948853},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5292999744415283},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.517300009727478},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.49950000643730164},{"id":"https://openalex.org/C2780870619","wikidata":"https://www.wikidata.org/wiki/Q48937708","display_name":"Quasinormal mode","level":3,"score":0.4828000068664551},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.46470001339912415},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.4641000032424927},{"id":"https://openalex.org/C82422596","wikidata":"https://www.wikidata.org/wiki/Q1094364","display_name":"Rotating black hole","level":3,"score":0.4442000091075897},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.413100004196167},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.3950999975204468},{"id":"https://openalex.org/C153013531","wikidata":"https://www.wikidata.org/wiki/Q1322810","display_name":"Scattering amplitude","level":3,"score":0.3693000078201294},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3684999942779541},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.36579999327659607},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.28760001063346863},{"id":"https://openalex.org/C190330329","wikidata":"https://www.wikidata.org/wiki/Q190035","display_name":"Gravitational wave","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2815000116825104},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.26989999413490295},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C126990412","wikidata":"https://www.wikidata.org/wiki/Q203218","display_name":"Spherical coordinate system","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1088/0264-9381/20/15/312","doi":"https://doi.org/10.1088/0264-9381/20/15/312","is_oa":true,"landing_page_url":"https://doi.org/10.1088/0264-9381/20/15/312","pdf_url":"https://iopscience.iop.org/article/10.1088/0264-9381/20/15/312/pdf","source":{"id":"https://openalex.org/S171172751","display_name":"Classical and Quantum Gravity","issn_l":"0264-9381","issn":["0264-9381","1361-6382"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","ki-jl-1","norway-1"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Classical and Quantum Gravity","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:gr-qc/0304030","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/gr-qc/0304030","pdf_url":"https://arxiv.org/pdf/gr-qc/0304030","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:eprints.soton.ac.uk:29451","doi":null,"is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/29451/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.gr-qc/0304030","doi":"https://doi.org/10.48550/arxiv.gr-qc/0304030","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.gr-qc/0304030","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":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1088/0264-9381/20/15/312","doi":"https://doi.org/10.1088/0264-9381/20/15/312","is_oa":true,"landing_page_url":"https://doi.org/10.1088/0264-9381/20/15/312","pdf_url":"https://iopscience.iop.org/article/10.1088/0264-9381/20/15/312/pdf","source":{"id":"https://openalex.org/S171172751","display_name":"Classical and Quantum Gravity","issn_l":"0264-9381","issn":["0264-9381","1361-6382"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","ki-jl-1","norway-1"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Classical and Quantum Gravity","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320321916","display_name":"State Scholarships Foundation","ror":"https://ror.org/023z3dm33"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2071917424.pdf","grobid_xml":"https://content.openalex.org/works/W2071917424.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W1964322120","https://openalex.org/W1968369949","https://openalex.org/W1969268076","https://openalex.org/W1971886890","https://openalex.org/W1973092187","https://openalex.org/W1974187409","https://openalex.org/W1977696161","https://openalex.org/W1980775018","https://openalex.org/W1988468538","https://openalex.org/W1988740911","https://openalex.org/W1995715342","https://openalex.org/W1997720720","https://openalex.org/W1999502447","https://openalex.org/W2001148114","https://openalex.org/W2010310369","https://openalex.org/W2011508391","https://openalex.org/W2012710252","https://openalex.org/W2013020265","https://openalex.org/W2013485448","https://openalex.org/W2013856706","https://openalex.org/W2017970833","https://openalex.org/W2022716862","https://openalex.org/W2025233220","https://openalex.org/W2028291513","https://openalex.org/W2028483511","https://openalex.org/W2034527135","https://openalex.org/W2039042696","https://openalex.org/W2040155109","https://openalex.org/W2046968225","https://openalex.org/W2047748745","https://openalex.org/W2048170417","https://openalex.org/W2050690415","https://openalex.org/W2051736254","https://openalex.org/W2055524364","https://openalex.org/W2067644039","https://openalex.org/W2069764580","https://openalex.org/W2077547356","https://openalex.org/W2080705137","https://openalex.org/W2088416579","https://openalex.org/W2107259515","https://openalex.org/W2107788712","https://openalex.org/W2128918391","https://openalex.org/W2137279971","https://openalex.org/W2168424351","https://openalex.org/W2176211596","https://openalex.org/W4295932358"],"related_works":[],"abstract_inverted_index":{"We":[0,140,191],"discuss":[1,41],"simple":[2],"integration":[3,68],"methods":[4],"for":[5,127,149,160,197,202,230],"the":[6,14,21,42,46,63,74,83,93,99,108,124,128,137,161,177,181,188,199,214,218,224,235],"calculation":[7],"of":[8,35,58,69,105,107,130,180],"black-hole":[9,163],"scattering":[10],"resonances":[11],"both":[12],"in":[13,92,123,213],"complex":[15,22,94,125],"frequency":[16],"plane":[17,25,126],"(quasinormal":[18],"modes)":[19],"and":[20,110,153,156,217],"angular":[23],"momentum":[24],"(Regge":[26],"poles).":[27],"Our":[28],"numerical":[29],"schemes":[30],"are":[31],"based":[32],"on":[33,223],"variations":[34],"'phase-amplitude'":[36],"methods.":[37],"In":[38],"particular,":[39],"we":[40],"Pr\u00fcfer":[43],"transformation,":[44],"where":[45],"original":[47],"(frequency":[48],"domain)":[49],"Teukolsky":[50],"wave":[51],"equation":[52],"is":[53,117,183,207],"replaced":[54],"by":[55,135,145,167],"a":[56,194],"pair":[57],"first-order":[59],"nonlinear":[60],"equations":[61],"governing":[62],"introduced":[64],"phase":[65],"functions.":[66],"Numerical":[67],"these":[70],"equations,":[71],"performed":[72],"along":[73,89],"real":[75,189],"r":[76,80,95],"\u2217":[77,81,96],"-axis":[78],"(where":[79],"denotes":[82],"usual":[84],"tortoise":[85],"radial":[86],"coordinate),":[87],"or":[88],"rotated":[90],"contours":[91],"-plane,":[97],"provides":[98],"required":[100],"-matrix":[101],"element":[102],"(the":[103],"ratio":[104],"amplitudes":[106],"outgoing":[109],"ingoing":[111],"waves":[112,211],"at":[113],"infinity).":[114],"M\u00fcller's":[115],"algorithm":[116],"then":[118],"employed":[119],"to":[120,171,209],"conduct":[121],"searches":[122],"poles":[129],"this":[131,143],"quantity":[132],"(which":[133],"are,":[134],"definition,":[136],"desired":[138],"resonances).":[139],"have":[141],"tested":[142],"method":[144,196,206],"verifying":[146],"known":[147],"results":[148,159,220],"Schwarzschild":[150],"quasinormal":[151,203,226],"modes":[152,227],"Regge":[154],"poles,":[155],"provide":[157],"new":[158,195],"Kerr":[162,215,237],"problem.":[164],"Results":[165],"produced":[166],"our":[168],"scheme":[169],"prove":[170],"be":[172],"accurate":[173],"as":[174,176],"long":[175],"imaginary":[178],"part":[179],"resonance":[182],"not":[184],"much":[185],"larger":[186],"than":[187],"part.":[190],"also":[192],"describe":[193],"estimating":[198],"'excitation":[200],"coefficients'":[201],"modes.":[204],"The":[205],"applied":[208],"scalar":[210],"moving":[212],"geometry,":[216],"obtained":[219],"shed":[221],"light":[222],"long-lived":[225],"that":[228],"exist":[229],"black":[231],"holes":[232],"rotating":[233],"near":[234],"extreme":[236],"limit.":[238]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":29},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-10-01T08:54:57.152042","created_date":"2016-06-24T00:00:00"}