{"id":"https://openalex.org/W7204802557","doi":"https://doi.org/10.48550/arxiv.2608.28186","title":"Photon Spheres and Shadows of Covariant Loop Quantum Black Holes in the general $\u03bc$-scheme","display_name":"Photon Spheres and Shadows of Covariant Loop Quantum Black Holes in the general $\u03bc$-scheme","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204802557","doi":"https://doi.org/10.48550/arxiv.2608.28186"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28186","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28186","pdf_url":"https://arxiv.org/pdf/2608.28186","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/2608.28186","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076714129","display_name":"Yu Han","orcid":"https://orcid.org/0000-0002-4266-7132","observed_orcids":["https://orcid.org/0000-0002-4266-7132"]},"institutions":[{"id":"https://openalex.org/I130750295","display_name":"Xinyang Normal University","ror":"https://ror.org/0190x2a66","country_code":"CN","type":"education","lineage":["https://openalex.org/I130750295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Han, Yu","raw_affiliation_strings":["College of Physics and Electrical Engineering , Xinyang Normal University , 464000 Xinyang , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Physics and Electrical Engineering , Xinyang Normal University , 464000 Xinyang , China","institution_ids":["https://openalex.org/I130750295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042410012","display_name":"\u5218\u5b5f","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Meng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5148762334","display_name":"Yongzhuang Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210096899","display_name":"Jiangsu University of Science and Technology","ror":"https://ror.org/00tyjp878","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210096899"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Yongzhuang","raw_affiliation_strings":["School of Science , Jiangsu University of Science and Technology , 212100 Zhenjiang , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science , Jiangsu University of Science and Technology , 212100 Zhenjiang , China","institution_ids":["https://openalex.org/I4210096899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.5863999724388123,"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"}},"topics":[{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.5863999724388123,"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":0.2012999951839447,"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/T10744","display_name":"Astrophysical Phenomena and Observations","score":0.14419999718666077,"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/black-hole-shadow","display_name":"black hole shadow","score":0.8740000128746033},{"id":"https://openalex.org/keywords/photon-sphere","display_name":"photon sphere","score":0.9660000205039978},{"id":"https://openalex.org/keywords/loop-quantum-gravity","display_name":"loop quantum gravity","score":0.843999981880188},{"id":"https://openalex.org/keywords/power-law-exponent","display_name":"flow index","score":0.4580000042915344},{"id":"https://openalex.org/keywords/lyapunov-exponents","display_name":"Lyapunov exponents","score":0.8360000252723694},{"id":"https://openalex.org/keywords/shadow-radius","display_name":"shadow radius","score":0.6589999794960022},{"id":"https://openalex.org/keywords/event-horizon-telescope-constraints","display_name":"Event Horizon Telescope constraints","score":0.7170000076293945}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7419000267982483},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.593500018119812},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5415999889373779},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.5400999784469604},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5375000238418579},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.512499988079071},{"id":"https://openalex.org/C148292158","wikidata":"https://www.wikidata.org/wiki/Q181741","display_name":"Event horizon","level":3,"score":0.5113000273704529},{"id":"https://openalex.org/C175757954","wikidata":"https://www.wikidata.org/wiki/Q2361910","display_name":"Photon sphere","level":5,"score":0.47690001130104065},{"id":"https://openalex.org/C84269361","wikidata":"https://www.wikidata.org/wiki/Q179235","display_name":"Phenomenology (philosophy)","level":2,"score":0.374099999666214},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3504999876022339},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32839998602867126},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3257000148296356},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.3192000091075897},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.2667999863624573}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28186","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28186","pdf_url":"https://arxiv.org/pdf/2608.28186","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.2608.28186","doi":"https://doi.org/10.48550/arxiv.2608.28186","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28186","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:2608.28186","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28186","pdf_url":"https://arxiv.org/pdf/2608.28186","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/F4320323845","display_name":"Natural Science Foundation of Henan Province","ror":null},{"id":"https://openalex.org/F4320327564","display_name":"Xinyang Normal University","ror":"https://ror.org/0190x2a66"},{"id":"https://openalex.org/F4320335834","display_name":"Nanhu Scholars Program for Young Scholars of Xinyang Normal University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204802557.pdf","grobid_xml":"https://content.openalex.org/works/W7204802557.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1602412994","https://openalex.org/W2013794521","https://openalex.org/W2031106768","https://openalex.org/W2052045615","https://openalex.org/W2060198182","https://openalex.org/W2085740659","https://openalex.org/W2109902906","https://openalex.org/W2123791503","https://openalex.org/W2147998383","https://openalex.org/W2149289292","https://openalex.org/W2159485102","https://openalex.org/W2252795400","https://openalex.org/W2798634036","https://openalex.org/W2806360372","https://openalex.org/W2936349953","https://openalex.org/W2947118958","https://openalex.org/W2973757829","https://openalex.org/W2990873960","https://openalex.org/W2996042325","https://openalex.org/W3035353170","https://openalex.org/W3049463193","https://openalex.org/W3161457974","https://openalex.org/W4206691163","https://openalex.org/W4221027780","https://openalex.org/W4221143712","https://openalex.org/W4226053022","https://openalex.org/W4229041459","https://openalex.org/W4280589633","https://openalex.org/W4313506310","https://openalex.org/W4323355237","https://openalex.org/W4382726611","https://openalex.org/W4392191146","https://openalex.org/W4394808211","https://openalex.org/W4403064306","https://openalex.org/W4409666037","https://openalex.org/W4410235083","https://openalex.org/W4410438280"],"related_works":["https://openalex.org/W3136457186","https://openalex.org/W4307466886","https://openalex.org/W7138896931","https://openalex.org/W4396566274","https://openalex.org/W7160275712","https://openalex.org/W4392546697","https://openalex.org/W3046482285","https://openalex.org/W3121628696","https://openalex.org/W4408424043","https://openalex.org/W2921861877"],"abstract_inverted_index":{"We":[0,129,178],"investigate":[1],"black":[2],"hole":[3],"shadows":[4],"and":[5,20,33,52,55,81,104,149,174,189,192,235],"photon":[6,74,106,117,134],"sphere":[7,75,107,118,135],"properties":[8],"for":[9,77,96,153,162,172,176,183],"two":[10],"families":[11],"of":[12,146,217],"covariant":[13],"quantum-corrected":[14],"black-hole":[15],"metrics":[16],"(hereafter":[17],"called":[18],"BH-I":[19],"BH-II)":[21],"formulated":[22],"within":[23],"a":[24,29,45,57,123,195,214],"general":[25,40],"$\u03bc$-scheme,":[26],"parameterised":[27],"by":[28,213],"power-law":[30],"exponent":[31],"$s$":[32,43,62,171],"an":[34,83,200],"amplitude":[35],"$\u03be$.":[36,98],"The":[37],"extension":[38],"to":[39,66],"(including":[41],"non-integer)":[42],"is":[44,63,94,136,239],"phenomenological":[46],"interpolation":[47],"between":[48],"the":[49,73,89,102,105,112,116,133,142,154,165,184,204,208,218,231],"$\u03bc_0$-scheme":[50],"($s=0$)":[51],"$\\bar\u03bc$-scheme":[53],"($s=1$)":[54],"reveals":[56],"rich":[58],"phenomenology":[59],"masked":[60],"when":[61,120],"usually":[64],"fixed":[65,163],"1":[67],"in":[68,111,203],"previous":[69],"literature.":[70],"For":[71,99],"BH-I,":[72],"exists":[76],"all":[78],"parameter":[79,114,144,158,233],"values":[80],"exhibits":[82],"exact":[84],"cancellation":[85],"at":[86],"$s=1$":[87],"where":[88],"coordinate":[90],"location":[91],"$r_{\\rm":[92],"ph}=3M$":[93],"restored":[95],"any":[97],"BH-II,":[100],"both":[101,147],"horizon":[103],"exhibit":[108],"critical":[109,125],"curves":[110],"$(\u03be,s)$":[113,206,232],"plane;":[115],"disappears":[119],"$\u03be$":[121,164],"exceeds":[122],"closed-form":[124,151],"value":[126],"$\u03be_c^{\\rm":[127],"PS}(s)$.":[128],"prove":[130],"analytically":[131],"that":[132,161,194,237],"always":[137],"unstable":[138],"($\u03bb_{\\rm":[139],"ph}>0$)":[140],"throughout":[141],"physical":[143],"space":[145,234],"metrics,":[148],"derive":[150,179,228],"expressions":[152],"Lyapunov":[155,190,219],"exponent.":[156,220],"Systematic":[157],"scans":[159],"reveal":[160],"shadow":[166,187,197],"radius":[167],"decreases":[168],"monotonically":[169],"with":[170],"BH-II":[173,238],"non-monotonically":[175],"BH-I.":[177,247],"small-parameter":[180],"analytic":[181],"expansions":[182],"photon-sphere":[185],"radius,":[186,188],"exponent,":[191],"demonstrate":[193],"single":[196],"measurement":[198,216],"suffers":[199],"observational":[201],"degeneracy":[202,209],"two-dimensional":[205],"space;":[207],"can":[210],"be":[211],"broken":[212],"simultaneous":[215],"Using":[221],"Event":[222],"Horizon":[223],"Telescope":[224],"(EHT)":[225],"measurements,":[226],"we":[227],"constraints":[229],"on":[230],"find":[236],"constrained":[240],"roughly":[241],"$2$--$4$":[242],"times":[243],"more":[244],"tightly":[245],"than":[246]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-01T00:00:00"}