{"id":"https://openalex.org/W7214804181","doi":"https://doi.org/10.48550/arxiv.2609.34957","title":"Horizon, Null-Orbit, and Photon-Sphere Phase Structures in Logarithmic Nonlinear Electrodynamics","display_name":"Horizon, Null-Orbit, and Photon-Sphere Phase Structures in Logarithmic Nonlinear Electrodynamics","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214804181","doi":"https://doi.org/10.48550/arxiv.2609.34957"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34957","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34957","pdf_url":"https://arxiv.org/pdf/2609.34957","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/2609.34957","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061971765","display_name":"Peshwaz Abdulkareem Abdoul","orcid":"https://orcid.org/0000-0002-2144-8336","observed_orcids":["https://orcid.org/0000-0002-2144-8336"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Abdoul, Peshwaz Abdulkareem","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5061971765"],"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":0.9804999828338623,"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":0.9804999828338623,"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":0.0052999998442828655,"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":0.0012000000569969416,"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/charged-black-holes","display_name":"charged black holes","score":0.7919999957084656},{"id":"https://openalex.org/keywords/asymptotically-flat-black-holes","display_name":"asymptotically flat black holes","score":0.8610000014305115},{"id":"https://openalex.org/keywords/null-geodesics","display_name":"null geodesics","score":0.6169999837875366},{"id":"https://openalex.org/keywords/photon-sphere","display_name":"photon sphere","score":0.6349999904632568},{"id":"https://openalex.org/keywords/horizonless-black-holes","display_name":"horizonless black holes","score":0.5339999794960022},{"id":"https://openalex.org/keywords/black-point","display_name":"black point","score":0.5049999952316284},{"id":"https://openalex.org/keywords/bifurcation-points","display_name":"bifurcation points","score":0.7379999756813049},{"id":"https://openalex.org/keywords/hawking-temperature","display_name":"Hawking temperature","score":0.6800000071525574},{"id":"https://openalex.org/keywords/black-hole-entropy","display_name":"black hole entropy","score":0.8199999928474426},{"id":"https://openalex.org/keywords/effective-potential","display_name":"effective potential","score":0.4099999964237213},{"id":"https://openalex.org/keywords/extremal-black-holes","display_name":"extremal black holes","score":0.5210000276565552}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7346000075340271},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5740000009536743},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.569599986076355},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.5002999901771545},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.460999995470047},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4189000129699707},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.4016999900341034},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.39640000462532043},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.38119998574256897},{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.36809998750686646},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.3675999939441681},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.36149999499320984},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2842999994754791},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34957","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34957","pdf_url":"https://arxiv.org/pdf/2609.34957","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.2609.34957","doi":"https://doi.org/10.48550/arxiv.2609.34957","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34957","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:2609.34957","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34957","pdf_url":"https://arxiv.org/pdf/2609.34957","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214804181.pdf","grobid_xml":"https://content.openalex.org/works/W7214804181.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1987560961","https://openalex.org/W2004245415","https://openalex.org/W2012572068","https://openalex.org/W2015762847","https://openalex.org/W2036238644","https://openalex.org/W2062833846","https://openalex.org/W2100194997","https://openalex.org/W2106778679","https://openalex.org/W2116359945","https://openalex.org/W2160712394","https://openalex.org/W2581807604","https://openalex.org/W2921854775","https://openalex.org/W2953265654","https://openalex.org/W2975951860","https://openalex.org/W3029948144","https://openalex.org/W3047808065","https://openalex.org/W3164153996","https://openalex.org/W4307981493","https://openalex.org/W4380988749","https://openalex.org/W4403321911","https://openalex.org/W4406759787","https://openalex.org/W4412950835","https://openalex.org/W4416683704","https://openalex.org/W7123786834","https://openalex.org/W7155701001","https://openalex.org/W7167846258"],"related_works":["https://openalex.org/W3157128328","https://openalex.org/W7167846258","https://openalex.org/W7165795842","https://openalex.org/W7155701001","https://openalex.org/W2953265654","https://openalex.org/W3036612975","https://openalex.org/W7154789442","https://openalex.org/W4391480599","https://openalex.org/W2567441220","https://openalex.org/W7164878355"],"abstract_inverted_index":{"We":[0,18],"investigate":[1],"static,":[2],"charged,":[3],"asymptotically":[4],"flat":[5],"black":[6,98,168],"holes":[7],"in":[8,97,196],"logarithmic":[9],"nonlinear":[10],"electrodynamics":[11],"(LNED)":[12],"within":[13],"the":[14,23,26,32,37,52,57,65,74,91,109,120,123,148,167,191,197],"$(Q,\u03b5)$":[15],"parameter":[16],"space.":[17],"distinguish":[19],"three":[20],"phase":[21],"structures:":[22,51],"horizon":[24,92],"geometry,":[25],"background":[27,58,129],"circular":[28,33],"null":[29],"orbits,":[30],"and":[31,56,112],"photon":[34,149,171],"orbits":[35],"of":[36,173],"effective":[38,75],"optical":[39,192],"geometry.":[40],"All":[41],"share":[42],"a":[43,143,155,158,163],"zero-radius":[44],"boundary":[45],"$Q_{nc}(\u03b5;M)=\u03b3M^{2/3}\u03b5^{1/6}$,":[46],"but":[47],"possess":[48],"distinct":[49],"critical":[50],"extremal":[53],"curve":[54,60,78],"$Q_{ext}(\u03b5;M)$":[55],"merger":[59,77],"$Q_{m}(\u03b5;M)$":[61],"both":[62,181],"terminate":[63],"at":[64,70,108,122,136,157],"bifurcation":[66,110,124],"point":[67,111,125],"$(Q_{b},\u03b5_{b})$,":[68],"located":[69],"$r=0$.":[71],"In":[72,146],"contrast,":[73,147],"photon-orbit":[76],"$Q_{m}^{ph}(\u03b5;M)$":[79],"does":[80,194],"not":[81],"pass":[82],"through":[83],"this":[84],"point.":[85],"For":[86],"$\u03b5\\ge\u03b5_{b}$,":[87,189],"approaching":[88],"$Q_{nc}$":[89],"shrinks":[90],"to":[93],"zero":[94],"radius,":[95,160],"resulting":[96],"points":[99,169],"with":[100,154],"non-zero,":[101],"quantum-corrected":[102],"entropy.":[103],"Their":[104],"Hawking":[105],"temperature":[106,121],"vanishes":[107],"diverges":[113],"for":[114,179,188],"$\u03b5>\u03b5_{b}$,":[115],"except":[116],"when":[117],"$\u03b7\u03b4=1$,":[118],"where":[119],"also":[126],"diverges.":[127],"The":[128],"potential":[130,150],"$V_{eff}^{bg}(r)$":[131],"develops":[132],"an":[133],"infinite":[134],"barrier":[135],"$r=0$":[137],"without":[138],"local":[139],"extrema,":[140],"acting":[141,161],"as":[142,162],"perfect":[144],"repeller.":[145],"$V_{eff}^{ph}(r)$":[151],"is":[152],"regularized":[153],"maximum":[156],"finite":[159,174],"partial":[164],"reflector.":[165],"Consequently,":[166],"retain":[170],"spheres":[172],"radius.":[175],"Away":[176],"from":[177],"$Q_{nc}$,":[178],"$\u03b5<\u03b5_{b}$,":[180],"geometries":[182],"support":[183],"horizonless":[184],"structures":[185],"above":[186],"$Q_{ext}$;":[187],"only":[190],"geometry":[193],"so":[195],"region":[198],"$Q_{nc}":[199]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-30T00:00:00"}
