{"id":"https://openalex.org/W2060745302","doi":"https://doi.org/10.1103/physrev.119.1743","title":"Maximal Extension of Schwarzschild Metric","display_name":"Maximal Extension of Schwarzschild Metric","publication_year":1960,"publication_date":"1960-09-01","ids":{"openalex":"https://openalex.org/W2060745302","doi":"https://doi.org/10.1103/physrev.119.1743","mag":"2060745302"},"language":"en","primary_location":{"id":"doi:10.1103/physrev.119.1743","doi":"https://doi.org/10.1103/physrev.119.1743","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrev.119.1743","pdf_url":null,"source":{"id":"https://openalex.org/S54862371","display_name":"Physical Review","issn_l":"0031-899X","issn":["0031-899X","1536-6065"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050146610","display_name":"Martin David Kruskal","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. D. Kruskal","raw_affiliation_strings":["Project Matterhorn, Princeton University, Princeton, New Jersey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Project Matterhorn, Princeton University, Princeton, New Jersey","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050146610"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":16.6877,"has_fulltext":false,"cited_by_count":986,"citation_normalized_percentile":{"value":0.98959975,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"119","issue":"5","first_page":"1743","last_page":"1745"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.8740000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.8740000128746033,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.09189999848604202,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.009600000455975533,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/schwarzschild-metric","display_name":"Schwarzschild metric","score":0.996999979019165},{"id":"https://openalex.org/keywords/maximal-extensions","display_name":"maximal extensions","score":0.8460000157356262},{"id":"https://openalex.org/keywords/coordinate-transformation","display_name":"coordinate transformation","score":0.6890000104904175},{"id":"https://openalex.org/keywords/singularity-removal","display_name":"singularity removal","score":0.7110000252723694},{"id":"https://openalex.org/keywords/black-hole-interior","display_name":"black hole interior","score":0.5260000228881836},{"id":"https://openalex.org/keywords/spacetime-singularities","display_name":"spacetime singularities","score":0.6520000100135803}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.7311710715293884},{"id":"https://openalex.org/C136125196","wikidata":"https://www.wikidata.org/wiki/Q742969","display_name":"Schwarzschild metric","level":3,"score":0.6643151044845581},{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.6238863468170166},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6166772842407227},{"id":"https://openalex.org/C114693822","wikidata":"https://www.wikidata.org/wiki/Q11757549","display_name":"Schwarzschild geodesics","level":5,"score":0.5783520936965942},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5377218127250671},{"id":"https://openalex.org/C95086748","wikidata":"https://www.wikidata.org/wiki/Q1068747","display_name":"Kerr metric","level":4,"score":0.5044244527816772},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4792052209377289},{"id":"https://openalex.org/C48286519","wikidata":"https://www.wikidata.org/wiki/Q461255","display_name":"Deriving the Schwarzschild solution","level":5,"score":0.45697033405303955},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3982114791870117},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3768419027328491},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.17902621626853943},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.1628488302230835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14527836441993713},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1103/physrev.119.1743","doi":"https://doi.org/10.1103/physrev.119.1743","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrev.119.1743","pdf_url":null,"source":{"id":"https://openalex.org/S54862371","display_name":"Physical Review","issn_l":"0031-899X","issn":["0031-899X","1536-6065"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1977702809","https://openalex.org/W2034066066","https://openalex.org/W2259553937","https://openalex.org/W2297596203","https://openalex.org/W2313896841","https://openalex.org/W4229824384"],"related_works":["https://openalex.org/W1992716937","https://openalex.org/W1621219740","https://openalex.org/W3045519983","https://openalex.org/W1670046030","https://openalex.org/W7052425903","https://openalex.org/W2028089254","https://openalex.org/W1653103389","https://openalex.org/W2081271554","https://openalex.org/W7097596464","https://openalex.org/W1803683497"],"abstract_inverted_index":{"There":[0],"is":[1,18,25],"presented":[2],"a":[3],"particularly":[4],"simple":[5],"transformation":[6],"of":[7],"the":[8,15,21],"Schwarzschild":[9],"metric":[10],"into":[11],"new":[12],"coordinates,":[13],"whereby":[14],"\"spherical":[16],"singularity\"":[17],"removed":[19],"and":[20],"maximal":[22],"singularity-free":[23],"extension":[24],"clearly":[26],"exhibited.":[27]},"counts_by_year":[{"year":2026,"cited_by_count":39},{"year":2025,"cited_by_count":56},{"year":2024,"cited_by_count":55},{"year":2023,"cited_by_count":35},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":28},{"year":2020,"cited_by_count":46},{"year":2019,"cited_by_count":132},{"year":2018,"cited_by_count":35},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":25},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":24}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}