{"id":"https://openalex.org/W3092853967","doi":"https://doi.org/10.3390/sym12101669","title":"On Schwarzschild\u2019s Interior Solution and Perfect Fluid Star Model","display_name":"On Schwarzschild\u2019s Interior Solution and Perfect Fluid Star Model","publication_year":2020,"publication_date":"2020-10-13","ids":{"openalex":"https://openalex.org/W3092853967","doi":"https://doi.org/10.3390/sym12101669","mag":"3092853967"},"language":"en","primary_location":{"id":"doi:10.3390/sym12101669","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101669","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1669/pdf?version=1603178232","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/10/1669/pdf?version=1603178232","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075542740","display_name":"Elisabetta Barletta","orcid":"https://orcid.org/0000-0002-6080-8613"},"institutions":[{"id":"https://openalex.org/I20272500","display_name":"University of Basilicata","ror":"https://ror.org/03tc05689","country_code":"IT","type":"education","lineage":["https://openalex.org/I20272500"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Elisabetta Barletta","raw_affiliation_strings":["Dipartimento di Matematica, Informatica, ed Economia, Universit\u00e0 degli Studi della Basilicata, 85100 Potenza, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Informatica, ed Economia, Universit\u00e0 degli Studi della Basilicata, 85100 Potenza, Italy","institution_ids":["https://openalex.org/I20272500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050669855","display_name":"Sorin Dragomir","orcid":"https://orcid.org/0000-0002-0886-0908"},"institutions":[{"id":"https://openalex.org/I20272500","display_name":"University of Basilicata","ror":"https://ror.org/03tc05689","country_code":"IT","type":"education","lineage":["https://openalex.org/I20272500"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Sorin Dragomir","raw_affiliation_strings":["Dipartimento di Matematica, Informatica, ed Economia, Universit\u00e0 degli Studi della Basilicata, 85100 Potenza, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Informatica, ed Economia, Universit\u00e0 degli Studi della Basilicata, 85100 Potenza, Italy","institution_ids":["https://openalex.org/I20272500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087153877","display_name":"Francesco Esposito","orcid":"https://orcid.org/0000-0002-3056-3627"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Esposito","raw_affiliation_strings":["Dipartimento di Matematica e Fisica <i>Ennio De Giorgi</i>, Universit\u00e0 del Salento, 73100 Lecce, Italy","Dipartimento di Matematica e Fisica Ennio De Giorgi, Universit\u00e0 del Salento, 73100 Lecce, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Fisica <i>Ennio De Giorgi</i>, Universit\u00e0 del Salento, 73100 Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Dipartimento di Matematica e Fisica Ennio De Giorgi, Universit\u00e0 del Salento, 73100 Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050669855"],"corresponding_institution_ids":["https://openalex.org/I20272500"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1366,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57591232,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"10","first_page":"1669","last_page":"1669"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9998999834060669,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9998999834060669,"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":0.9998000264167786,"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/schwarzschild-radius","display_name":"Schwarzschild radius","score":0.8084486722946167},{"id":"https://openalex.org/keywords/schwarzschild-metric","display_name":"Schwarzschild metric","score":0.7763901948928833},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6917461156845093},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.6193141341209412},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5445828437805176},{"id":"https://openalex.org/keywords/gravitational-field","display_name":"Gravitational field","score":0.532578706741333},{"id":"https://openalex.org/keywords/star","display_name":"Star (game theory)","score":0.523430585861206},{"id":"https://openalex.org/keywords/gravitation","display_name":"Gravitation","score":0.48320186138153076},{"id":"https://openalex.org/keywords/perfect-fluid","display_name":"Perfect fluid","score":0.47905170917510986},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.44878318905830383},{"id":"https://openalex.org/keywords/deriving-the-schwarzschild-solution","display_name":"Deriving the Schwarzschild solution","score":0.4234023690223694},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3345346748828888},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.289980411529541},{"id":"https://openalex.org/keywords/general-relativity","display_name":"General relativity","score":0.28713083267211914},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.22616681456565857},{"id":"https://openalex.org/keywords/kerr-metric","display_name":"Kerr metric","score":0.2179812788963318},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1602117419242859},{"id":"https://openalex.org/keywords/astrophysics","display_name":"Astrophysics","score":0.14739546179771423}],"concepts":[{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.8084486722946167},{"id":"https://openalex.org/C136125196","wikidata":"https://www.wikidata.org/wiki/Q742969","display_name":"Schwarzschild metric","level":3,"score":0.7763901948928833},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6917461156845093},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.6193141341209412},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5445828437805176},{"id":"https://openalex.org/C14257148","wikidata":"https://www.wikidata.org/wiki/Q558066","display_name":"Gravitational field","level":2,"score":0.532578706741333},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.523430585861206},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.48320186138153076},{"id":"https://openalex.org/C52220454","wikidata":"https://www.wikidata.org/wiki/Q613845","display_name":"Perfect fluid","level":2,"score":0.47905170917510986},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44878318905830383},{"id":"https://openalex.org/C48286519","wikidata":"https://www.wikidata.org/wiki/Q461255","display_name":"Deriving the Schwarzschild solution","level":5,"score":0.4234023690223694},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3345346748828888},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.289980411529541},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.28713083267211914},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.22616681456565857},{"id":"https://openalex.org/C95086748","wikidata":"https://www.wikidata.org/wiki/Q1068747","display_name":"Kerr metric","level":4,"score":0.2179812788963318},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1602117419242859},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.14739546179771423}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym12101669","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101669","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1669/pdf?version=1603178232","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d47403d132ca4107858786e7fe9bf784","is_oa":true,"landing_page_url":"https://doaj.org/article/d47403d132ca4107858786e7fe9bf784","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 10, p 1669 (2020)","raw_type":"article"},{"id":"pmh:oai:iris.unibas.it:11563/146848","is_oa":true,"landing_page_url":"http://hdl.handle.net/11563/146848","pdf_url":null,"source":{"id":"https://openalex.org/S4377196360","display_name":"CINECA IRIS Institutional Research Information System (University of Basilicata)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20272500","host_organization_name":"University of Basilicata","host_organization_lineage":["https://openalex.org/I20272500"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/10/1669/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12101669","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12101669","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101669","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1669/pdf?version=1603178232","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3092853967.pdf","grobid_xml":"https://content.openalex.org/works/W3092853967.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W119556221","https://openalex.org/W1978395617","https://openalex.org/W1993158470","https://openalex.org/W2016735301","https://openalex.org/W2027184145","https://openalex.org/W2032881480","https://openalex.org/W2040236652","https://openalex.org/W2097523349","https://openalex.org/W2117839321","https://openalex.org/W2147998383","https://openalex.org/W2487865073","https://openalex.org/W3004121687","https://openalex.org/W3023684895","https://openalex.org/W3101413008","https://openalex.org/W3108114178","https://openalex.org/W6677432034"],"related_works":["https://openalex.org/W4296012609","https://openalex.org/W2915673819","https://openalex.org/W17899771","https://openalex.org/W799717315","https://openalex.org/W2091356062","https://openalex.org/W2134160070","https://openalex.org/W2024418890","https://openalex.org/W2045886921","https://openalex.org/W1928693544","https://openalex.org/W1978395617"],"abstract_inverted_index":{"We":[0,36,92],"solve":[1],"the":[2,12,17,49,60,65,81,86,99,126,130,139],"boundary":[3,50],"value":[4],"problem":[5],"for":[6,69,113],"Einstein\u2019s":[7],"gravitational":[8,66],"field":[9,29,67],"equations":[10,68],"in":[11,16,32,109,133,145],"presence":[13],"of":[14,19,24,41,117,129,135,138],"matter":[15],"form":[18],"an":[20],"incompressible":[21],"perfect":[22,88],"fluid":[23,89],"density":[25],"\u03c1":[26],"and":[27,43,53,77,105,142],"pressure":[28],"p(r)":[30],"located":[31],"a":[33,38,70],"ball":[34],"r\u2264r0.":[35],"find":[37],"1-parameter":[39],"family":[40],"time-independent":[42],"radially":[44],"symmetric":[45],"solutions":[46,111],"ga,\u03c1a,pa:\u22122m&lt;a&lt;a1":[47],"satisfying":[48],"conditions":[51],"g=gS":[52],"p=0":[54],"on":[55],"r=r0,":[56],"where":[57],"gS":[58],"is":[59,107],"exterior":[61],"Schwarzschild":[62,83],"solution":[63],"(solving":[64],"point":[71],"mass":[72],"M":[73],"concentrated":[74],"at":[75],"r=0)":[76],"containing":[78],"(for":[79],"a=0)":[80],"interior":[82],"solution,":[84],"i.e.,":[85],"classical":[87],"star":[90,121],"model.":[91],"show":[93],"that":[94,103],"Schwarzschild\u2019s":[95],"requirement":[96],"r0&gt;9\u03baM/(4c2)":[97],"identifies":[98],"\u201cphysical\u201d":[100],"(i.e.,":[101],"such":[102],"pa(r)\u22650":[104],"pa(r)":[106],"bounded":[108],"0\u2264r\u2264r0)":[110],"{pa:a\u2208U0}":[112],"some":[114],"neighbourhood":[115],"U0\u2282(\u22122m,+\u221e)":[116],"a=0.":[118],"For":[119],"every":[120],"model":[122],"{ga:a0&lt;a&lt;a1},":[123],"we":[124],"compute":[125],"volume":[127],"V(a)":[128],"region":[131],"r\u2264r0":[132],"terms":[134],"abelian":[136],"integrals":[137],"first,":[140],"second,":[141],"third":[143],"kind":[144],"Legendre":[146],"form.":[147]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}