{"id":"https://openalex.org/W7225829891","doi":"https://doi.org/10.1142/s0219887827500319","title":"Self-Similar Vector Fields and Curvature Properties of Bianchi Type V Spacetime with Imperfect Fluid Sources","display_name":"Self-Similar Vector Fields and Curvature Properties of Bianchi Type V Spacetime with Imperfect Fluid Sources","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225829891","doi":"https://doi.org/10.1142/s0219887827500319"},"language":"en","primary_location":{"id":"doi:10.1142/s0219887827500319","doi":"https://doi.org/10.1142/s0219887827500319","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219887827500319","pdf_url":null,"source":{"id":"https://openalex.org/S146144561","display_name":"International Journal of Geometric Methods in Modern Physics","issn_l":"0219-8878","issn":["0219-8878","1793-6977"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geometric Methods in Modern Physics","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/A5101990465","display_name":"Tahir Hussain","orcid":"https://orcid.org/0000-0003-2303-760X","observed_orcids":["https://orcid.org/0000-0003-2303-760X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tahir Hussain","raw_affiliation_strings":["https://orcid.org/0000-0003-2303-760X"],"raw_orcid":"https://orcid.org/0000-0003-2303-760X","affiliations":[{"raw_affiliation_string":"https://orcid.org/0000-0003-2303-760X","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065963378","display_name":"Saba Ghaffar","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saba Ghaffar","raw_affiliation_strings":[""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063805354","display_name":"Fawad Khan","orcid":"https://orcid.org/0000-0003-2252-6655","observed_orcids":["https://orcid.org/0000-0003-2252-6655"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fawad Khan","raw_affiliation_strings":[""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140325793","display_name":"Naveed Ahmad","orcid":"https://orcid.org/0000-0003-0336-1453","observed_orcids":["https://orcid.org/0000-0003-0336-1453"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Naveed Ahmad","raw_affiliation_strings":[""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024886105","display_name":"Abdulkarim Alansari","orcid":"https://orcid.org/0000-0003-0028-1685","observed_orcids":["https://orcid.org/0000-0003-0028-1685"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abdulkarim Alansari","raw_affiliation_strings":[""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.5371000170707703,"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"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.5371000170707703,"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"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.38499999046325684,"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":0.061799999326467514,"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":[],"concepts":[{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.7505000233650208},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.7138000130653381},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.6320000290870667},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5626000165939331},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5393999814987183},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.531000018119812},{"id":"https://openalex.org/C108804581","wikidata":"https://www.wikidata.org/wiki/Q5447001","display_name":"Field equation","level":2,"score":0.5044000148773193},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.48840001225471497},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.46959999203681946},{"id":"https://openalex.org/C52220454","wikidata":"https://www.wikidata.org/wiki/Q613845","display_name":"Perfect fluid","level":2,"score":0.4562999904155731},{"id":"https://openalex.org/C42519931","wikidata":"https://www.wikidata.org/wiki/Q1200279","display_name":"Killing vector field","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.424699991941452},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4052000045776367},{"id":"https://openalex.org/C154693114","wikidata":"https://www.wikidata.org/wiki/Q6796059","display_name":"Maxwell's equations in curved spacetime","level":5,"score":0.39879998564720154},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.37119999527931213},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C2780791080","wikidata":"https://www.wikidata.org/wiki/Q273711","display_name":"Einstein field equations","level":3,"score":0.3628999888896942},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.3492000102996826},{"id":"https://openalex.org/C20892832","wikidata":"https://www.wikidata.org/wiki/Q3271879","display_name":"Circular symmetry","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3384000062942505},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C65305961","wikidata":"https://www.wikidata.org/wiki/Q7572737","display_name":"Spacetime symmetries","level":5,"score":0.3050999939441681},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30079999566078186},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.27799999713897705}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219887827500319","doi":"https://doi.org/10.1142/s0219887827500319","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219887827500319","pdf_url":null,"source":{"id":"https://openalex.org/S146144561","display_name":"International Journal of Geometric Methods in Modern Physics","issn_l":"0219-8878","issn":["0219-8878","1793-6977"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geometric Methods in Modern Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"explores":[2],"self-similar":[3],"vector":[4,36],"fields":[5],"(SSVFs)":[6],"of":[7,31,48,62,71,97,102,134],"Bianchi":[8],"type":[9],"V":[10],"spacetime":[11,64],"using":[12],"the":[13,21,28,32,39,45,51,54,63,68,72,90,94,100,108,120],"Rif":[14,55],"tree":[15,56],"approach.":[16],"The":[17],"symmetry":[18,52],"equations":[19,111],"governing":[20],"SSVFs":[22,40],"are":[23,75,117],"systematically":[24],"solved":[25],"to":[26,119],"derive":[27],"explicit":[29],"form":[30],"metric":[33],"coefficients":[34],"and":[35,82,93,104,132],"fields,":[37],"classifying":[38],"into":[41,89],"various":[42],"kinds.":[43],"Unlike":[44],"conventional":[46],"method":[47],"directly":[49],"integrating":[50],"equations,":[53],"approach":[57],"ensures":[58],"a":[59],"comprehensive":[60],"classification":[61],"under":[65],"consideration.":[66],"Additionally,":[67],"curvature":[69,92],"properties":[70,126],"derived":[73],"metrics":[74],"explored":[76],"by":[77],"finding":[78],"their":[79],"corresponding":[80],"Kretschmann":[81],"Gauss-Bonnet":[83],"invariants.":[84],"These":[85],"invariants":[86],"provide":[87],"insight":[88],"total":[91],"geometric":[95],"characteristics":[96],"spacetime,":[98],"revealing":[99,123],"influence":[101],"temporal":[103],"spatial":[105],"expansions.":[106],"Moreover,":[107],"Einstein's":[109],"field":[110],"with":[112],"an":[113],"imperfect":[114],"fluid":[115],"source":[116],"applied":[118],"obtained":[121],"metrics,":[122],"specific":[124],"physical":[125],"such":[127],"as":[128],"energy":[129],"density,":[130],"pressure,":[131],"equation":[133],"state.":[135]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}