{"id":"https://openalex.org/W7204871287","doi":"https://doi.org/10.48550/arxiv.2608.30950","title":"Saha's ionization in the Schwarzschild spacetime","display_name":"Saha's ionization in the Schwarzschild spacetime","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204871287","doi":"https://doi.org/10.48550/arxiv.2608.30950"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30950","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30950","pdf_url":"https://arxiv.org/pdf/2608.30950","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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/2608.30950","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119688689","display_name":"L\u00e1zaro L. Sales","orcid":"https://orcid.org/0000-0002-5352-6642","observed_orcids":["https://orcid.org/0000-0002-5352-6642"]},"institutions":[{"id":"https://openalex.org/I41455075","display_name":"Universidade Federal de Campina Grande","ror":"https://ror.org/00eftnx64","country_code":"BR","type":"education","lineage":["https://openalex.org/I41455075"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Sales, L\u00e1zaro L.","raw_affiliation_strings":["Departamento de F\u00edsica , Universidade Federal de Campina Grande , Caixa Postal 10071 , 58429-900 , Campina Grande , Para\u00edba , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica , Universidade Federal de Campina Grande , Caixa Postal 10071 , 58429-900 , Campina Grande , Para\u00edba , Brazil","institution_ids":["https://openalex.org/I41455075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148915307","display_name":"Jonatas A. Silva","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210103065","display_name":"Universidade do Estado do Rio Grande do Norte","ror":"https://ror.org/01ee0g236","country_code":"BR","type":"education","lineage":["https://openalex.org/I4210103065"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Silva, Jonatas A.","raw_affiliation_strings":["Departamento de F\u00edsica , Universidade do Estado do Rio Grande do Norte , 59610-210 , Mossor\u00f3-RN , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica , Universidade do Estado do Rio Grande do Norte , 59610-210 , Mossor\u00f3-RN , Brazil","institution_ids":["https://openalex.org/I4210103065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056853859","display_name":"Amilcar R. de Queiroz","orcid":"https://orcid.org/0000-0002-4785-5589","observed_orcids":["https://orcid.org/0000-0002-4785-5589"]},"institutions":[{"id":"https://openalex.org/I41455075","display_name":"Universidade Federal de Campina Grande","ror":"https://ror.org/00eftnx64","country_code":"BR","type":"education","lineage":["https://openalex.org/I41455075"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Queiroz, Amilcar R.","raw_affiliation_strings":["Departamento de F\u00edsica , Universidade Federal de Campina Grande , Caixa Postal 10071 , 58429-900 , Campina Grande , Para\u00edba , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica , Universidade Federal de Campina Grande , Caixa Postal 10071 , 58429-900 , Campina Grande , Para\u00edba , Brazil","institution_ids":["https://openalex.org/I41455075"]}]}],"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.6996999979019165,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.6996999979019165,"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":0.08910000324249268,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.07440000027418137,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/schwarzschild-metric","display_name":"Schwarzschild metric","score":0.9909999966621399},{"id":"https://openalex.org/keywords/gravitational-redshift","display_name":"gravitational redshift","score":0.9070000052452087},{"id":"https://openalex.org/keywords/maxwell-boltzmann-distribution","display_name":"Maxwell-Boltzmann distribution","score":0.902999997138977},{"id":"https://openalex.org/keywords/maxwell-juttner-distribution","display_name":"Maxwell-J\u00fcttner distribution","score":0.9779999852180481},{"id":"https://openalex.org/keywords/ionization-fraction","display_name":"ionization fraction","score":0.8330000042915344},{"id":"https://openalex.org/keywords/static-gravitational-field","display_name":"static gravitational field","score":0.5329999923706055},{"id":"https://openalex.org/keywords/neutral-hydrogen","display_name":"neutral hydrogen","score":0.5040000081062317},{"id":"https://openalex.org/keywords/nonrelativistic-limit","display_name":"non-relativistic limit","score":0.6639999747276306}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8237000107765198},{"id":"https://openalex.org/C198291218","wikidata":"https://www.wikidata.org/wiki/Q190382","display_name":"Ionization","level":3,"score":0.6273000240325928},{"id":"https://openalex.org/C14257148","wikidata":"https://www.wikidata.org/wiki/Q558066","display_name":"Gravitational field","level":2,"score":0.5971999764442444},{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.5758000016212463},{"id":"https://openalex.org/C180547424","wikidata":"https://www.wikidata.org/wiki/Q656181","display_name":"Gravitational redshift","level":3,"score":0.5382000207901001},{"id":"https://openalex.org/C33024259","wikidata":"https://www.wikidata.org/wiki/Q76250","display_name":"Redshift","level":3,"score":0.5120000243186951},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.45649999380111694},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.40529999136924744},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.3912000060081482},{"id":"https://openalex.org/C136125196","wikidata":"https://www.wikidata.org/wiki/Q742969","display_name":"Schwarzschild metric","level":3,"score":0.3743000030517578},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.34200000762939453},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.3206999897956848},{"id":"https://openalex.org/C22492302","wikidata":"https://www.wikidata.org/wiki/Q2297853","display_name":"Gravitational energy","level":3,"score":0.31779998540878296},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.31349998712539673},{"id":"https://openalex.org/C81263218","wikidata":"https://www.wikidata.org/wiki/Q7330289","display_name":"Relativistic quantum chemistry","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.28349998593330383},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.2696000039577484},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C32127712","wikidata":"https://www.wikidata.org/wiki/Q3366867","display_name":"Test particle","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C147192597","wikidata":"https://www.wikidata.org/wiki/Q483769","display_name":"Ionization energy","level":4,"score":0.2639000117778778},{"id":"https://openalex.org/C44715290","wikidata":"https://www.wikidata.org/wiki/Q13012237","display_name":"Numerical relativity","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.25769999623298645}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30950","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30950","pdf_url":"https://arxiv.org/pdf/2608.30950","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.30950","doi":"https://doi.org/10.48550/arxiv.2608.30950","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30950","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30950","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30950","pdf_url":"https://arxiv.org/pdf/2608.30950","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323351","display_name":"Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Estado da Para\u00edba","ror":"https://ror.org/021y4b202"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204871287.pdf","grobid_xml":"https://content.openalex.org/works/W7204871287.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2784514488","https://openalex.org/W7116100547"],"related_works":["https://openalex.org/W2784514488","https://openalex.org/W4376855089","https://openalex.org/W4400383808","https://openalex.org/W2075198548","https://openalex.org/W2138100528","https://openalex.org/W2125184722","https://openalex.org/W1983917515","https://openalex.org/W3151717403","https://openalex.org/W1987338171","https://openalex.org/W1643160230"],"abstract_inverted_index":{"We":[0,63,110,143],"investigate":[1],"the":[2,7,13,22,27,39,49,54,66,70,74,78,82,87,93,105,113,117,120,124,129,133,140,146,152,165,190],"Saha":[3,71,108],"ionization":[4,55,118,126,134,181],"equilibrium":[5,91,182],"in":[6,36,97,164,183],"exterior":[8],"Schwarzschild":[9,40],"spacetime.":[10],"Starting":[11],"from":[12,123],"mass-shell":[14],"condition":[15],"for":[16],"a":[17,137,177,184],"massive":[18],"particle,":[19],"we":[20],"derive":[21],"conserved":[23],"energy":[24,44],"associated":[25],"with":[26],"timelike":[28],"Killing":[29],"symmetry":[30],"and":[31,81,89,128,155,188,196],"obtain":[32],"its":[33,159],"nonrelativistic":[34],"limit":[35],"terms":[37,98],"of":[38,76,99,116,132,139,180,199],"lapse":[41],"function.":[42],"This":[43],"is":[45,162,171],"then":[46],"incorporated":[47],"into":[48],"Maxwell--Boltzmann":[50],"distribution":[51,154],"to":[52,104],"construct":[53],"balance":[56],"as":[57,136],"seen":[58],"by":[59],"an":[60],"asymptotic":[61,141],"observer.":[62],"show":[64,156],"that":[65,158],"gravitational":[67,114,186,193],"field":[68,187],"modifies":[69],"relation":[72],"through":[73],"redshift":[75,115,194],"both":[77],"particle":[79],"energies":[80],"thermodynamic":[83],"variables.":[84],"By":[85],"imposing":[86],"Tolman--Ehrenfest":[88],"Klein":[90],"conditions,":[92],"formulation":[94],"expressed":[95],"entirely":[96],"locally":[100],"measured":[101],"quantities":[102],"reduces":[103],"standard":[106],"flat-spacetime":[107,125],"equation.":[109],"further":[111],"analyze":[112],"energy,":[119],"relative":[121],"departure":[122],"ratio,":[127],"corresponding":[130],"shift":[131],"fraction":[135],"function":[138],"temperature.":[142],"also":[144],"present":[145],"relativistic":[147],"classical":[148],"counterpart":[149],"based":[150],"on":[151],"Maxwell--J\u00fcttner":[153],"explicitly":[157],"leading":[160],"correction":[161],"negligible":[163],"temperature":[166],"range":[167],"where":[168],"neutral":[169],"hydrogen":[170],"appreciably":[172],"abundant.":[173],"These":[174],"results":[175],"provide":[176],"consistent":[178],"description":[179],"static":[185],"clarify":[189],"distinction":[191],"between":[192],"effects":[195],"intrinsic":[197],"modifications":[198],"local":[200],"atomic":[201],"physics.":[202]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
