{"id":"https://openalex.org/W7166803858","doi":"https://doi.org/10.48550/arxiv.2606.30798","title":"As Cold as a Black Hole: Extended Photon Spheres","display_name":"As Cold as a Black Hole: Extended Photon Spheres","publication_year":2026,"publication_date":"2026-06-29","ids":{"openalex":"https://openalex.org/W7166803858","doi":"https://doi.org/10.48550/arxiv.2606.30798"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2606.30798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.30798","pdf_url":"https://arxiv.org/pdf/2606.30798","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/2606.30798","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015637395","display_name":"Marcos Riojas","orcid":"https://orcid.org/0000-0002-2411-1333","observed_orcids":["https://orcid.org/0000-0002-2411-1333"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Riojas, Marcos","raw_affiliation_strings":["Center for the Fundamental Laws of Nature , Harvard University , Cambridge , MA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for the Fundamental Laws of Nature , Harvard University , Cambridge , MA , USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015637395"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.006399999838322401,"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":0.0020000000949949026,"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-thermodynamics","display_name":"black hole thermodynamics","score":0.800000011920929},{"id":"https://openalex.org/keywords/israel-junction-conditions","display_name":"Israel junction conditions","score":0.7770000100135803},{"id":"https://openalex.org/keywords/tolman-oppenheimer-volkoff-equations","display_name":"Tolman-Oppenheimer-Volkoff equations","score":0.9990000128746033},{"id":"https://openalex.org/keywords/hawking-temperature","display_name":"Hawking temperature","score":0.8100000023841858},{"id":"https://openalex.org/keywords/specific-heat-capacity","display_name":"specific heat","score":0.675000011920929},{"id":"https://openalex.org/keywords/thermodynamic-entropy","display_name":"thermodynamic entropy","score":0.7260000109672546},{"id":"https://openalex.org/keywords/photon-ring","display_name":"photon ring","score":0.8159999847412109},{"id":"https://openalex.org/keywords/self-similar-solutions","display_name":"self-similar solutions","score":0.8820000290870667},{"id":"https://openalex.org/keywords/frozen-stars","display_name":"frozen stars","score":0.9779999852180481}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7946000099182129},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.6187999844551086},{"id":"https://openalex.org/C175757954","wikidata":"https://www.wikidata.org/wiki/Q2361910","display_name":"Photon sphere","level":5,"score":0.5961999893188477},{"id":"https://openalex.org/C54937798","wikidata":"https://www.wikidata.org/wiki/Q2024141","display_name":"Massless particle","level":2,"score":0.5327000021934509},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.49549999833106995},{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.4772999882698059},{"id":"https://openalex.org/C40745267","wikidata":"https://www.wikidata.org/wiki/Q497396","display_name":"Hawking radiation","level":3,"score":0.4530999958515167},{"id":"https://openalex.org/C136125196","wikidata":"https://www.wikidata.org/wiki/Q742969","display_name":"Schwarzschild metric","level":3,"score":0.429500013589859},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.42250001430511475},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4178999960422516},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4004000127315521},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.39419999718666077},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.39160001277923584},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.37130001187324524},{"id":"https://openalex.org/C89394759","wikidata":"https://www.wikidata.org/wiki/Q192593","display_name":"Thermal radiation","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.33090001344680786},{"id":"https://openalex.org/C157909335","wikidata":"https://www.wikidata.org/wiki/Q900097","display_name":"Black-body radiation","level":3,"score":0.3246000111103058},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C144951741","wikidata":"https://www.wikidata.org/wiki/Q131468","display_name":"White hole","level":3,"score":0.31029999256134033},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C29310469","wikidata":"https://www.wikidata.org/wiki/Q3175122","display_name":"Thermal equilibrium","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.2912999987602234},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.25850000977516174}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2606.30798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.30798","pdf_url":"https://arxiv.org/pdf/2606.30798","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.2606.30798","doi":"https://doi.org/10.48550/arxiv.2606.30798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.30798","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:2606.30798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.30798","pdf_url":"https://arxiv.org/pdf/2606.30798","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/F4320309622","display_name":"Harvard University","ror":"https://ror.org/03vek6s52"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7166803858.pdf","grobid_xml":"https://content.openalex.org/works/W7166803858.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W2011646003","https://openalex.org/W2017236921","https://openalex.org/W2064777467","https://openalex.org/W2095721433","https://openalex.org/W2120923477","https://openalex.org/W2129190302","https://openalex.org/W2132072001","https://openalex.org/W2139496359","https://openalex.org/W2166248051","https://openalex.org/W2950107180","https://openalex.org/W4309238312"],"related_works":["https://openalex.org/W7166867909","https://openalex.org/W7012583813","https://openalex.org/W7223096579","https://openalex.org/W7160290632","https://openalex.org/W2000325016","https://openalex.org/W3202994924","https://openalex.org/W4415024917","https://openalex.org/W1573354391","https://openalex.org/W2739171502","https://openalex.org/W2031326898"],"abstract_inverted_index":{"It":[0],"is":[1,34,73,97],"widely":[2],"believed":[3],"that":[4,35,128],"self-gravitating":[5],"radiation":[6],"cannot":[7],"reach":[8],"thermal":[9],"equilibrium":[10],"with":[11,122],"a":[12,21,129],"black":[13,51,131,138],"hole":[14,52,139],"in":[15,150],"asymptotically":[16],"flat":[17],"spacetime.":[18],"We":[19],"describe":[20],"marginally":[22],"stable":[23],"continuum":[24],"exception":[25,115],"to":[26,75,105],"the":[27,36,40,45,54,65,70,85,93,110,182,206,212],"standard":[28],"instability":[29],"argument.":[30],"Our":[31],"main":[32],"observation":[33],"photon":[37,71,147,186,217],"sphere":[38,72],"controls":[39],"Israel":[41],"junction":[42],"conditions":[43],"(IJCs),":[44],"Tolman-Oppenheimer-Volkoff":[46],"(TOV)":[47],"equation,":[48],"and":[49,56,77,90,173,180,228],"finite-radius":[50],"thermodynamics:":[53],"IJCs":[55],"TOV":[57],"equation":[58],"are":[59,164,188],"equivalent":[60],"at":[61,69,80,211],"zero":[62],"radial":[63],"pressure,":[64],"inverse":[66],"specific":[67,95],"heat":[68,96],"proportional":[74],"$-\u039b$,":[76],"adding":[78],"shells":[79],"fixed":[81],"total":[82],"mass":[83,141],"\\textit{lowers}":[84],"asymptotic":[86],"Hawking":[87,145],"temperature":[88],"if":[89,92],"only":[91],"local":[94],"positive.":[98],"Using":[99],"these":[100,162],"results,":[101],"we":[102,126,160],"show":[103,161],"how":[104],"compute":[106],"thermodynamic":[107,174,178],"entropies":[108],"without":[109],"Euclidean":[111],"path":[112],"integral.":[113],"The":[114],"described":[116],"here":[117],"results":[118],"from":[119,170],"companion":[120],"work":[121],"M.J.":[123],"Strassler,":[124],"where":[125],"found":[127],"\"hillingar":[130],"hole\"":[132],"(HBH)":[133],"mimics":[134],"an":[135],"ordinary":[136],"Schwarzschild":[137],"of":[140,184,198,203,214],"$M$,":[142],"sharing":[143],"its":[144,152],"temperature,":[146],"ring,":[148],"and,":[149],"equilibrium,":[151],"coarse-grained":[153],"entropy":[154],"$S":[155],"=":[156],"4":[157],"\u03c0M^2$.":[158],"Here,":[159],"features":[163],"not":[165],"tuned;":[166],"they":[167,193],"follow":[168],"uniquely":[169],"joint":[171],"mechanical":[172],"constraints.":[175],"Conditions":[176],"for":[177,181,190],"mimicry":[179],"formation":[183],"extended":[185,216],"spheres":[187,218],"found;":[189],"self-similar":[191,199],"solutions":[192],"coincide.":[194],"A":[195],"one-parameter":[196],"family":[197,224],"systems":[200],"--":[201,219],"all":[202],"which,":[204],"excepting":[205],"HBH,":[207],"require":[208],"massless":[209],"walls":[210],"edges":[213],"their":[215],"satisfies":[220],"both":[221],"conditions.":[222],"This":[223],"includes":[225],"\"stiffest":[226],"stars\"":[227],"\"frozen":[229],"stars\".":[230]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-07-02T00:00:00"}