{"id":"https://openalex.org/W7130856474","doi":"https://doi.org/10.5281/zenodo.18725098","title":"The Modified Schwarzschild Radius with Hubble Field and its Connection to Dark Matter","display_name":"The Modified Schwarzschild Radius with Hubble Field and its Connection to Dark Matter","publication_year":2026,"publication_date":"2026-02-21","ids":{"openalex":"https://openalex.org/W7130856474","doi":"https://doi.org/10.5281/zenodo.18725098"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.18725098","doi":"https://doi.org/10.5281/zenodo.18725098","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18725098","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.18725098","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087424686","display_name":"H. F\u00fcrstenau","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"F\u00fcrstenau, Hermann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5087424686"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15221141,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9945999979972839,"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":0.9945999979972839,"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/T11090","display_name":"Dark Matter and Cosmic Phenomena","score":0.0013000000035390258,"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/T10026","display_name":"Galaxies: Formation, Evolution, Phenomena","score":0.0012000000569969416,"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/hubble-expansion","display_name":"Hubble expansion","score":0.7929999828338623},{"id":"https://openalex.org/keywords/dark-matter","display_name":"dark matter","score":0.7559999823570251},{"id":"https://openalex.org/keywords/escape-velocity","display_name":"escape velocity","score":0.7099999785423279},{"id":"https://openalex.org/keywords/cosmological-black-holes","display_name":"cosmological black holes","score":0.5820000171661377},{"id":"https://openalex.org/keywords/dark-matter-abundance","display_name":"dark matter abundance","score":0.5619999766349792},{"id":"https://openalex.org/keywords/hubble-constant","display_name":"Hubble constant","score":0.492000013589859}],"concepts":[{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.8924999833106995},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8705000281333923},{"id":"https://openalex.org/C61969629","wikidata":"https://www.wikidata.org/wiki/Q911640","display_name":"Hubble volume","level":5,"score":0.6876999735832214},{"id":"https://openalex.org/C103874350","wikidata":"https://www.wikidata.org/wiki/Q179916","display_name":"Hubble's law","level":4,"score":0.5608999729156494},{"id":"https://openalex.org/C20154449","wikidata":"https://www.wikidata.org/wiki/Q1129469","display_name":"Metric expansion of space","level":4,"score":0.46480000019073486},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C136125196","wikidata":"https://www.wikidata.org/wiki/Q742969","display_name":"Schwarzschild metric","level":3,"score":0.4431999921798706},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.4050000011920929},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.39399999380111694},{"id":"https://openalex.org/C159249277","wikidata":"https://www.wikidata.org/wiki/Q79925","display_name":"Dark matter","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C125860484","wikidata":"https://www.wikidata.org/wiki/Q500699","display_name":"Age of the universe","level":4,"score":0.36800000071525574},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3513000011444092},{"id":"https://openalex.org/C166861157","wikidata":"https://www.wikidata.org/wiki/Q59151","display_name":"Cosmological constant","level":2,"score":0.3472999930381775},{"id":"https://openalex.org/C172790937","wikidata":"https://www.wikidata.org/wiki/Q18343","display_name":"Dark energy","level":3,"score":0.3301999866962433},{"id":"https://openalex.org/C126320844","wikidata":"https://www.wikidata.org/wiki/Q1153477","display_name":"Cold dark matter","level":3,"score":0.31850001215934753},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2797999978065491},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.27900001406669617},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C144386022","wikidata":"https://www.wikidata.org/wiki/Q1332997","display_name":"Scale factor (cosmology)","level":5,"score":0.2703000009059906},{"id":"https://openalex.org/C166126730","wikidata":"https://www.wikidata.org/wiki/Q725309","display_name":"Planck","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2624000012874603},{"id":"https://openalex.org/C128228380","wikidata":"https://www.wikidata.org/wiki/Q468999","display_name":"Planck mass","level":3,"score":0.25459998846054077},{"id":"https://openalex.org/C29761201","wikidata":"https://www.wikidata.org/wiki/Q5223514","display_name":"Dark fluid","level":4,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.18725098","doi":"https://doi.org/10.5281/zenodo.18725098","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18725098","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.18725099","doi":"https://doi.org/10.5281/zenodo.18725099","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18725099","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.18725098","doi":"https://doi.org/10.5281/zenodo.18725098","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18725098","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"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":{"The":[0,47,212],"classical":[1,144],"Schwarzschild":[2,33,120,159],"radius":[3,34,121,126],"defines":[4],"the":[5,21,31,37,42,51,65,72,78,84,93,97,114,118,123,134,137,143,153,157,164,175,184,191,206],"boundary":[6,154],"at":[7],"which":[8],"an":[9,16,180],"object":[10],"becomes":[11],"a":[12,55,171,215],"black":[13,145],"hole.":[14],"In":[15],"expanding":[17],"universe":[18],"governed":[19],"by":[20,35,156],"Hubble":[22,39,135,176],"flow,":[23],"this":[24,75,187,199,203],"concept":[25],"must":[26],"be":[27,170],"generalized.":[28],"We":[29],"derive":[30],"modified":[32,119,158],"including":[36,189],"repulsive":[38],"potential":[40],"into":[41,57],"escape":[43],"velocity":[44],"condition":[45],"v=c.":[46],"resulting":[48],"expression":[49],"separates":[50],"total":[52],"mass":[53,193],"of":[54,96,174,186],"system":[56],"two":[58],"distinct":[59],"terms:":[60],"one":[61,69],"scaling":[62,70],"linearly":[63],"with":[64,71,113],"radius,":[66],"M_1\u221dR,":[67],"and":[68,201,221],"volume,":[73],"M_2\u221dH^2\u22c5R^3.Applying":[74],"decomposition":[76],"to":[77,205],"Universe":[79,138],"itself,":[80],"we":[81,104],"find":[82],"that":[83,163],"ratio":[85,115],"M_2/M_1":[86],"=H^2\u22c5R^2/c^2":[87],"\u2261\u03b6":[88],"is":[89,109,127,194],"not":[90],"arbitrary.":[91],"Using":[92],"precise":[94],"measurements":[95],"Planck":[98],"mission":[99],"(\u03a9_vis/\u03a9_tot=0,049,":[100],"\u03a9_(E_dark":[101],")/\u03a9_tot=0,683,":[102],"\u03a9_dark/\u03a9_tot=0,268),":[103],"obtain":[105],"\u03b6=5,47\u00b10,1.":[106],"This":[107,161],"value":[108],"in":[110],"excellent":[111],"agreement":[112],"derived":[116],"from":[117],"when":[122],"Universe's":[124,192],"effective":[125],"taken":[128],"as":[129],"R=c/(H_0\u22c5":[130],"\u03b6)\u22482,2\u22c510^26":[131],"m.Remarkably,":[132],"without":[133],"modification,":[136],"would":[139],"lie":[140],"deep":[141],"inside":[142],"hole":[146],"region.":[147],"Instead,":[148],"it":[149],"resides":[150],"exactly":[151],"on":[152],"defined":[155],"radius.":[160],"suggests":[162],"observed":[165],"dark":[166],"matter":[167],"abundance":[168],"may":[169],"direct":[172],"consequence":[173],"expansion":[177],"rather":[178],"than":[179],"exotic":[181],"particle.We":[182],"discuss":[183],"implications":[185],"result,":[188],"whether":[190],"constant":[195],"or":[196],"dynamically":[197],"tracks":[198],"boundary,":[200],"how":[202],"relates":[204],"Rest":[207],"Angular":[208],"Momentum":[209],"(RAM)":[210],"model.":[211],"findings":[213],"provide":[214],"novel,":[216],"testable":[217],"link":[218],"between":[219],"cosmology":[220],"observations.":[222]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-02-22T00:00:00"}
