{"id":"https://openalex.org/W7214110371","doi":"https://doi.org/10.48550/arxiv.2609.25110","title":"A Closed-Form Master Solution for Gravitational Decoupling of a Unified Family of Isotropic Stellar Seeds","display_name":"A Closed-Form Master Solution for Gravitational Decoupling of a Unified Family of Isotropic Stellar Seeds","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214110371","doi":"https://doi.org/10.48550/arxiv.2609.25110"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25110","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25110","pdf_url":"https://arxiv.org/pdf/2609.25110","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.25110","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052579556","display_name":"a Santanu Pradhan","orcid":"https://orcid.org/0000-0002-1932-8431","observed_orcids":["https://orcid.org/0000-0002-1932-8431"]},"institutions":[{"id":"https://openalex.org/I82571370","display_name":"GLA University","ror":"https://ror.org/05fnxgv12","country_code":"IN","type":"education","lineage":["https://openalex.org/I82571370"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pradhan, Anirudh","raw_affiliation_strings":["Centre for Cosmology , Astrophysics and Space Science , GLA University , Mathura -281 406 , Uttar Pradesh , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Cosmology , Astrophysics and Space Science , GLA University , Mathura -281 406 , Uttar Pradesh , India","institution_ids":["https://openalex.org/I82571370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122183810","display_name":"Safiqul Islam","orcid":"https://orcid.org/0000-0003-1373-4137","observed_orcids":["https://orcid.org/0000-0003-1373-4137"]},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Islam, Safiqul","raw_affiliation_strings":["Department of Mathematics and Statistics , College of Science , King Faisal University , P.O. Box 400 , Al Ahsa 31982 , Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , College of Science , King Faisal University , P.O. Box 400 , Al Ahsa 31982 , Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152568357","display_name":"Ajit Kumar","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I134705546","display_name":"Teerthanker Mahaveer University","ror":"https://ror.org/04vkd2013","country_code":"IN","type":"education","lineage":["https://openalex.org/I134705546"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kumar, Ajit","raw_affiliation_strings":["Department of Mathematics , Faculty of Engineering , Teerthanker Mahaveer University , Moradabad - 244001 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Faculty of Engineering , Teerthanker Mahaveer University , Moradabad - 244001 , India","institution_ids":["https://openalex.org/I134705546"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5128752472","display_name":"Muhammad Aamir","orcid":"https://orcid.org/0000-0002-5782-0064","observed_orcids":["https://orcid.org/0000-0002-5782-0064"]},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Aamir, Muhammad","raw_affiliation_strings":["Department of Physics , College of Science , King Faisal University , P.O. Box 400 , Al Ahsa 31982 , Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , College of Science , King Faisal University , P.O. Box 400 , Al Ahsa 31982 , Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.9434000253677368,"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/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.9434000253677368,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.01549999974668026,"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":0.008799999952316284,"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/anisotropic-compact-stars","display_name":"anisotropic compact stars","score":0.8579999804496765},{"id":"https://openalex.org/keywords/minimal-geometric-deformation","display_name":"minimal geometric deformation","score":0.9470000267028809},{"id":"https://openalex.org/keywords/gravitational-decoupling","display_name":"gravitational decoupling","score":0.7910000085830688},{"id":"https://openalex.org/keywords/analytical-solution","display_name":"analytical solution","score":0.5690000057220459},{"id":"https://openalex.org/keywords/gaussian-hypergeometric-function","display_name":"Gauss hypergeometric function","score":0.9390000104904175},{"id":"https://openalex.org/keywords/schwarzschild-exterior","display_name":"Schwarzschild exterior","score":0.8840000033378601},{"id":"https://openalex.org/keywords/causality","display_name":"causality","score":0.574999988079071},{"id":"https://openalex.org/keywords/tidal-love-numbers","display_name":"tidal Love numbers","score":0.8930000066757202},{"id":"https://openalex.org/keywords/tidal-deformability","display_name":"tidal deformability","score":0.9660000205039978}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.7258999943733215},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.661899983882904},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6194000244140625},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.5615000128746033},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.5205000042915344},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4616999924182892},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.43869999051094055},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.40290001034736633},{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.35519999265670776},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C150846664","wikidata":"https://www.wikidata.org/wiki/Q7602306","display_name":"Stars","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.296099990606308},{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.28700000047683716},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2802000045776367},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2782000005245209},{"id":"https://openalex.org/C118396296","wikidata":"https://www.wikidata.org/wiki/Q329273","display_name":"Gravitational collapse","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C2776716506","wikidata":"https://www.wikidata.org/wiki/Q5161158","display_name":"Conjugate points","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C18444321","wikidata":"https://www.wikidata.org/wiki/Q368442","display_name":"Compact star","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C136125196","wikidata":"https://www.wikidata.org/wiki/Q742969","display_name":"Schwarzschild metric","level":3,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25110","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25110","pdf_url":"https://arxiv.org/pdf/2609.25110","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":"doi:10.48550/arxiv.2609.25110","doi":"https://doi.org/10.48550/arxiv.2609.25110","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25110","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.25110","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25110","pdf_url":"https://arxiv.org/pdf/2609.25110","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331156","display_name":"King Faisal University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214110371.pdf","grobid_xml":"https://content.openalex.org/works/W7214110371.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W2022144662","https://openalex.org/W2132072001","https://openalex.org/W2741543132","https://openalex.org/W2798461589","https://openalex.org/W2887564369","https://openalex.org/W2952273155","https://openalex.org/W2963246914","https://openalex.org/W2965853030","https://openalex.org/W2979655805","https://openalex.org/W2996750695","https://openalex.org/W3013264998","https://openalex.org/W3014240063","https://openalex.org/W3032895275","https://openalex.org/W3033891070","https://openalex.org/W3037287379","https://openalex.org/W3180378010","https://openalex.org/W4309918931"],"related_works":["https://openalex.org/W4200262024","https://openalex.org/W4387159973","https://openalex.org/W3012826612","https://openalex.org/W2898677646","https://openalex.org/W7202171785","https://openalex.org/W2947137617","https://openalex.org/W2915025853","https://openalex.org/W4404385203","https://openalex.org/W2887564369","https://openalex.org/W3003092964"],"abstract_inverted_index":{"We":[0,103],"present":[1],"a":[2,17,58,167,217],"unification":[3],"scheme":[4],"for":[5,86,141],"anisotropic":[6,90,107,152],"compact":[7],"stars":[8],"generated":[9],"via":[10],"minimal":[11],"geometric":[12],"deformation":[13],"(MGD),":[14],"built":[15],"on":[16],"two-parameter":[18],"seed":[19,212],"family":[20,39,95],"$\u03bd(r)=\\text{Ln}[C(1+ar^{2n})^{m}]$":[21],"whose":[22],"radial":[23],"metric":[24],"potential":[25],"$\u03bc(r)=e^{-\u03bb(r)}$":[26],"is":[27,57,96],"fixed":[28,214],"in":[29,75,78,135,224],"closed":[30,76],"form":[31],"by":[32,166],"the":[33,38,50,62,72,81,89,93,105,110,114,119,127,132,142,175,181,188,198,203,210,221,225],"isotropy":[34],"condition.":[35],"At":[36],"$n=1$":[37,94],"reproduces":[40],"Tolman":[41,145],"IV,":[42],"Korkina--Orlyanskii,":[43],"Heintzmann":[44,159,226],"IIa,":[45],"and":[46,118,130,137,147,161,193,227],"Durgapal":[47,162,228],"IV--V":[48,163],"as":[49],"particular":[51],"cases":[52],"$m=1,2,3,4,5$.":[53],"The":[54],"key":[55],"result":[56],"single":[59],"closure":[60],"of":[61,80,92,122,174],"MGD":[63],"$\u03b8$-sector,":[64],"through":[65],"one":[66,100],"source":[67],"function":[68,84],"$g(r)$,":[69],"that":[70,202],"integrates":[71],"decoupler":[73],"equation":[74],"form,":[77],"terms":[79],"Gauss":[82],"hypergeometric":[83],"${}_2F_1$,":[85],"\\emph{arbitrary}":[87],"$(n,m)$:":[88],"extension":[91],"thus":[97],"obtained":[98],"from":[99],"master":[101],"formula.":[102],"derive":[104],"effective":[106],"matter":[108,184],"content,":[109,185],"Darmois--Israel":[111],"matching":[112],"to":[113,209],"exterior":[115],"Schwarzschild":[116],"vacuum,":[117],"full":[120],"set":[121],"physical":[123],"acceptability":[124],"criteria":[125],"constraining":[126],"parameter":[128,177],"space,":[129],"map":[131],"admissible":[133,199],"region":[134],"compactness":[136,168],"decoupling":[138,176,204],"strength":[139],"explicitly":[140],"case":[143],"$n=1$:":[144],"IV":[146],"Korkina--Orlyanskii":[148],"admit":[149],"physically":[150],"consistent":[151],"deformations":[153],"at":[154,213],"arbitrarily":[155],"high":[156],"compactness,":[157,215],"while":[158],"IIa":[160],"are":[164],"bounded":[165],"ceiling":[169,223],"beyond":[170],"which":[171],"no":[172],"value":[173],"restores":[178],"causality.":[179],"Using":[180],"same":[182],"closed-form":[183],"we":[186],"compute":[187],"quadrupolar":[189],"tidal":[190,195],"Love":[191],"number":[192],"dimensionless":[194],"deformability":[196],"across":[197],"region,":[200],"finding":[201],"systematically":[205],"enhances":[206],"both":[207],"relative":[208],"isotropic":[211],"with":[216],"sharp":[218],"rise":[219],"near":[220],"causal":[222],"branches.":[229]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-24T00:00:00"}
