{"id":"https://openalex.org/W2147683021","doi":"https://doi.org/10.1140/epjc/s10052-015-3300-5","title":"Generalized Sparling\u2013Thirring form in the Brans\u2013Dicke theory","display_name":"Generalized Sparling\u2013Thirring form in the Brans\u2013Dicke theory","publication_year":2015,"publication_date":"2015-02-01","ids":{"openalex":"https://openalex.org/W2147683021","doi":"https://doi.org/10.1140/epjc/s10052-015-3300-5","mag":"2147683021"},"language":"en","primary_location":{"id":"doi:10.1140/epjc/s10052-015-3300-5","doi":"https://doi.org/10.1140/epjc/s10052-015-3300-5","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjc/s10052-015-3300-5","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-015-3300-5.pdf","source":{"id":"https://openalex.org/S94052278","display_name":"The European Physical Journal C","issn_l":"1434-6044","issn":["1434-6044","1434-6052"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-2","ki-jl-1","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal C","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-015-3300-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102967166","display_name":"Ahmet Baykal","orcid":"https://orcid.org/0000-0003-0362-9544","observed_orcids":["https://orcid.org/0000-0003-0362-9544"]},"institutions":[{"id":"https://openalex.org/I198265615","display_name":"Ni\u011fde \u00d6mer Halisdemir \u00dcniversitesi","ror":"https://ror.org/03ejnre35","country_code":"TR","type":"education","lineage":["https://openalex.org/I198265615"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ahmet Baykal","raw_affiliation_strings":["Department of Physics, Faculty of Arts and Sciences, Ni\u011fde University, Bor Yolu, 51240, Ni\u011fde, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Faculty of Arts and Sciences, Ni\u011fde University, Bor Yolu, 51240, Ni\u011fde, Turkey","institution_ids":["https://openalex.org/I198265615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021462289","display_name":"\u00d6zg\u00fcr Delice","orcid":"https://orcid.org/0000-0001-9494-8617","observed_orcids":["https://orcid.org/0000-0001-9494-8617"]},"institutions":[{"id":"https://openalex.org/I74897591","display_name":"Marmara University","ror":"https://ror.org/02kswqa67","country_code":"TR","type":"education","lineage":["https://openalex.org/I74897591"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"\u00d6zg\u00fcr Delice","raw_affiliation_strings":["Department of Physics, Faculty of Arts and Sciences, Marmara University, 34722, Istanbul, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Faculty of Arts and Sciences, Marmara University, 34722, Istanbul, Turkey","institution_ids":["https://openalex.org/I74897591"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021462289"],"corresponding_institution_ids":["https://openalex.org/I74897591"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05128977,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"75","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9657999873161316,"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":0.9657999873161316,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.02710000053048134,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.002300000051036477,"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/brans-dicke-theory","display_name":"Brans-Dicke theory","score":0.9990000128746033},{"id":"https://openalex.org/keywords/superpotential","display_name":"superpotential","score":0.9449999928474426},{"id":"https://openalex.org/keywords/energy-definition","display_name":"energy definition","score":0.41600000858306885},{"id":"https://openalex.org/keywords/jordan-frame","display_name":"Jordan frame","score":0.9829999804496765},{"id":"https://openalex.org/keywords/einstein-frame","display_name":"Einstein frame","score":0.9990000128746033},{"id":"https://openalex.org/keywords/scalar-tensor-gravity","display_name":"scalar-tensor gravity","score":0.6240000128746033},{"id":"https://openalex.org/keywords/field-equations","display_name":"field equations","score":0.550000011920929}],"concepts":[{"id":"https://openalex.org/C168948012","wikidata":"https://www.wikidata.org/wiki/Q3978010","display_name":"Superpotential","level":3,"score":0.9513999819755554},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.6402999758720398},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.49559998512268066},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4884999990463257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48590001463890076},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4787999987602234},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3986999988555908},{"id":"https://openalex.org/C187268509","wikidata":"https://www.wikidata.org/wiki/Q1402884","display_name":"Field theory (psychology)","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3783999979496002},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3677000105381012},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.3562999963760376},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C2778975207","wikidata":"https://www.wikidata.org/wiki/Q7078836","display_name":"Of the form","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28439998626708984},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C108804581","wikidata":"https://www.wikidata.org/wiki/Q5447001","display_name":"Field equation","level":2,"score":0.26809999346733093}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1140/epjc/s10052-015-3300-5","doi":"https://doi.org/10.1140/epjc/s10052-015-3300-5","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjc/s10052-015-3300-5","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-015-3300-5.pdf","source":{"id":"https://openalex.org/S94052278","display_name":"The European Physical Journal C","issn_l":"1434-6044","issn":["1434-6044","1434-6052"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-2","ki-jl-1","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal C","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1410.4134","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1410.4134","pdf_url":"https://arxiv.org/pdf/1410.4134","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:edpsciences.org:dkey/10.1140/epjc/s10052-015-3300-5","doi":null,"is_oa":false,"landing_page_url":"http://www.springerlink.com/content/fulltext.pdf?id=doi:10.1140/epjc/s10052-015-3300-5","pdf_url":"http://www.springerlink.com/content/fulltext.pdf?id=doi:10.1140/epjc/s10052-015-3300-5","source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1140/epjc/s10052-015-3300-5","raw_type":"Text"},{"id":"pmh:oai:openaccess.marmara.edu.tr:11424/245597","doi":null,"is_oa":true,"landing_page_url":"https://openaccess.marmara.edu.tr/bitstreams/78c543a5-5eaa-48f1-9867-ac6b2f0773a3/download","pdf_url":null,"source":{"id":"https://openalex.org/S4306401380","display_name":"Dspace Repository (Marmara \u00dcniversitesi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I74897591","host_organization_name":"Marmara University","host_organization_lineage":["https://openalex.org/I74897591"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:acikerisim.ohu.edu.tr:11480/15663","doi":null,"is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjc/s10052-015-3300-5","pdf_url":null,"source":{"id":"https://openalex.org/S7407055360","display_name":"Ni\u011fde \u00dcniversitesi A\u00e7\u0131k Eri\u015fim Sistemi","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:openaccess.marmara.edu.tr:11424/101395","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11424/101395","pdf_url":null,"source":{"id":"https://openalex.org/S4306401380","display_name":"Dspace Repository (Marmara \u00dcniversitesi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I74897591","host_organization_name":"Marmara University","host_organization_lineage":["https://openalex.org/I74897591"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:openaccess.marmara.edu.tr:11424/109763","doi":null,"is_oa":true,"landing_page_url":"https://www.scopus.com/inward/record.url?eid=2-s2.0-84923066155&partnerID=40&md5=c1e0d26039a69c2aecf81ecb736d10e0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401380","display_name":"Dspace Repository (Marmara \u00dcniversitesi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I74897591","host_organization_name":"Marmara University","host_organization_lineage":["https://openalex.org/I74897591"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"doi:10.48550/arxiv.1410.4134","doi":"https://doi.org/10.48550/arxiv.1410.4134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1410.4134","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":"doi:10.1140/epjc/s10052-015-3300-5","doi":"https://doi.org/10.1140/epjc/s10052-015-3300-5","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjc/s10052-015-3300-5","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-015-3300-5.pdf","source":{"id":"https://openalex.org/S94052278","display_name":"The European Physical Journal C","issn_l":"1434-6044","issn":["1434-6044","1434-6052"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-2","ki-jl-1","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal C","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2147683021.pdf","grobid_xml":"https://content.openalex.org/works/W2147683021.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W1549581905","https://openalex.org/W1774692326","https://openalex.org/W1791150725","https://openalex.org/W1937221913","https://openalex.org/W1970153976","https://openalex.org/W1971799102","https://openalex.org/W1978667315","https://openalex.org/W1984464449","https://openalex.org/W1986415873","https://openalex.org/W1986669506","https://openalex.org/W1987955826","https://openalex.org/W1989589910","https://openalex.org/W1989972931","https://openalex.org/W1998871856","https://openalex.org/W2004188331","https://openalex.org/W2007022730","https://openalex.org/W2013479398","https://openalex.org/W2016201553","https://openalex.org/W2025307991","https://openalex.org/W2035762303","https://openalex.org/W2036317464","https://openalex.org/W2037506073","https://openalex.org/W2039214790","https://openalex.org/W2039909064","https://openalex.org/W2048950741","https://openalex.org/W2050862563","https://openalex.org/W2052679646","https://openalex.org/W2067477988","https://openalex.org/W2070228627","https://openalex.org/W2072219271","https://openalex.org/W2072612440","https://openalex.org/W2076144303","https://openalex.org/W2078556844","https://openalex.org/W2080300410","https://openalex.org/W2108594325","https://openalex.org/W2111166811","https://openalex.org/W2123823073","https://openalex.org/W2156031765","https://openalex.org/W2156078230","https://openalex.org/W2162976779","https://openalex.org/W2173018294","https://openalex.org/W2174188461","https://openalex.org/W2187943790","https://openalex.org/W2328674408","https://openalex.org/W2485066948","https://openalex.org/W3025198550","https://openalex.org/W3095389225","https://openalex.org/W3103592616","https://openalex.org/W4229558079"],"related_works":["https://openalex.org/W4391046942","https://openalex.org/W7095295014","https://openalex.org/W2086400484","https://openalex.org/W1840793735","https://openalex.org/W2299648442","https://openalex.org/W376651014","https://openalex.org/W2781516809","https://openalex.org/W1984333067","https://openalex.org/W2802118134","https://openalex.org/W2143713242"],"abstract_inverted_index":{"The":[0,31],"definition":[1],"of":[2],"the":[3,13,37,40,48,52,62,70,73],"Sparling\u2013Thirring":[4,64],"form":[5,28,65],"is":[6,43,66],"extended":[7],"to":[8,47,57,68],"Brans\u2013Dicke":[9,14,79],"theory.":[10,80],"By":[11],"writing":[12],"field":[15],"equations":[16],"in":[17,39,45,51,78],"a":[18,22,25],"formally":[19],"Maxwell-like":[20],"form,":[21],"superpotential":[23,38],"and":[24],"corresponding":[26,49],"pseudo-energy-momentum":[27],"are":[29],"defined.":[30],"general":[32],"energy":[33,71],"expression":[34,50],"provided":[35],"by":[36],"Jordan":[41],"frame":[42],"discussed":[44],"relation":[46],"Einstein":[53],"frame.":[54],"In":[55],"order":[56],"substantiate":[58],"its":[59],"formal":[60],"definition,":[61],"generalized":[63],"used":[67],"calculate":[69],"for":[72],"spherically":[74],"symmetric":[75],"vacuum":[76],"solution":[77]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2016-06-24T00:00:00"}