{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T05:16:58Z","timestamp":1768281418196,"version":"3.49.0"},"reference-count":55,"publisher":"IOP Publishing","issue":"15","license":[{"start":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T00:00:00Z","timestamp":1753660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T00:00:00Z","timestamp":1753660800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["PTDC\/FIS-AST\/0054\/2021"],"award-info":[{"award-number":["PTDC\/FIS-AST\/0054\/2021"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Class. Quantum Grav."],"published-print":{"date-parts":[[2025,8,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider a recently introduced extension of General Relativity based on the use of the Cotton tensor and dubbed as Cotton gravity, to estimate the size of a new constant <jats:italic>\u03b3<\/jats:italic> appearing within a spherically symmetric, vacuum solution of such theory. Taking into account its non-asymptotically flat character, we use the inferred size of the central brightness depression of the supermassive object at the heart of the Milky Way galaxy (Sgr A*) by the Event Horizon Telescope to constrain at 2<jats:italic>\u03c3<\/jats:italic>) the CG parameter as <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:mi>\u03b3<\/mml:mi>\n                           <mml:mi>M<\/mml:mi>\n                           <mml:mo>\u2248<\/mml:mo>\n                           <mml:mn>3.5<\/mml:mn>\n                           <mml:mo>\u00d7<\/mml:mo>\n                           <mml:msup>\n                              <mml:mn>10<\/mml:mn>\n                              <mml:mrow>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mn>12<\/mml:mn>\n                              <\/mml:mrow>\n                           <\/mml:msup>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula>. We study the potential observational consequences from the smallness of such a value using exact and numerical expressions for the deflection angle, optical images from optically and geometrically thin accretion disks, isoradials, and instability scales (Lyapunov index) of nearly bound geodesics associated to photon rings. Our results point towards the impossibility to distinguish between these two geometries using current and foreseeable techniques in the field of interferometric detection of optical sources.<\/jats:p>","DOI":"10.1088\/1361-6382\/adf0ba","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T22:55:29Z","timestamp":1752706529000},"page":"155012","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Constraints on the <i>\u03b3<\/i>-parameter for the vacuum solution of Cotton gravity with geodesics and shadows"],"prefix":"10.1088","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7230-3666","authenticated-orcid":true,"given":"Ednaldo L B","family":"Junior","sequence":"first","affiliation":[]},{"given":"Jos\u00e9 Tarciso S S","family":"Junior","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9388-8373","authenticated-orcid":true,"given":"Francisco S N","family":"Lobo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8586-0285","authenticated-orcid":true,"given":"Manuel E","family":"Rodrigues","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3984-9864","authenticated-orcid":true,"given":"Diego","family":"Rubiera-Garcia","sequence":"additional","affiliation":[]},{"given":"Lu\u00eds F","family":"Dias da Silva","sequence":"additional","affiliation":[]},{"given":"Henrique A","family":"Vieira","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2025,7,28]]},"reference":[{"key":"cqgadf0babib1","doi-asserted-by":"publisher","first-page":"4","DOI":"10.12942\/lrr-2014-4","volume":"17","author":"Will","year":"2014","journal-title":"Living Rev. Relativ."},{"key":"cqgadf0babib2","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1086\/300499","volume":"116","author":"Supernova Search Team","year":"1998","journal-title":"Astron. J."},{"key":"cqgadf0babib3","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1086\/307221","volume":"517","author":"Supernova Cosmology Project","year":"1999","journal-title":"Astrophys. J."},{"key":"cqgadf0babib4","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s10714-022-03038-8","volume":"54","author":"Senovilla","year":"2022","journal-title":"Rel. Gravit."},{"key":"cqgadf0babib5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.72.084013","volume":"72","author":"Hawking","year":"2005","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib6","author":"Rovelli","year":"2004"},{"key":"cqgadf0babib7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2012.01.001","volume":"513","author":"Clifton","year":"2012","journal-title":"Phys. Rep."},{"key":"cqgadf0babib8","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.physrep.2011.09.003","volume":"509","author":"Capozziello","year":"2011","journal-title":"Phys. Rep."},{"key":"cqgadf0babib9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.L121502","volume":"103","author":"Harada","year":"2021","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.106.064044","volume":"106","author":"Harada","year":"2022","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib11","author":"Sussman"},{"key":"cqgadf0babib12","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/ad1781","volume":"41","author":"Gogberashvili","year":"2024","journal-title":"Class. Quantum Gravit."},{"key":"cqgadf0babib13","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/s10714-023-03106-7","volume":"55","author":"Mantica","year":"2023","journal-title":"Rel. Grav."},{"key":"cqgadf0babib14","author":"Sussman"},{"key":"cqgadf0babib15","author":"Congdon","year":"2018"},{"key":"cqgadf0babib16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.66.103001","volume":"66","author":"Bozza","year":"2002","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib17","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1088\/0004-637X\/753\/1\/56","volume":"753","author":"Bozza","year":"2012","journal-title":"Astrophys. J."},{"key":"cqgadf0babib18","doi-asserted-by":"publisher","first-page":"JCAP12(2022)018","DOI":"10.1088\/1475-7516\/2022\/12\/018","author":"Pietroni","year":"2022","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"cqgadf0babib19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.102.104029","volume":"102","author":"Tsukamoto","year":"2020","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.024033","volume":"103","author":"Tsukamoto","year":"2021","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.104.124016","volume":"104","author":"Tsukamoto","year":"2021","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib22","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1140\/epjc\/s10052-022-10441-7","volume":"82","author":"Zhang","year":"2022","journal-title":"Eur. Phys. J. C"},{"key":"cqgadf0babib23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.024018","volume":"100","author":"Gralla","year":"2019","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib24","doi-asserted-by":"publisher","first-page":"L13","DOI":"10.1086\/312423","volume":"528","author":"Falcke","year":"2000","journal-title":"Astrophys. J. Lett."},{"key":"cqgadf0babib25","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1007\/s10714-018-2361-9","volume":"50","author":"Cunha","year":"2018","journal-title":"Gen. Rel. Grav."},{"key":"cqgadf0babib26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.044031","volume":"101","author":"Gralla","year":"2020","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib27","doi-asserted-by":"publisher","first-page":"eaaz1310","DOI":"10.1126\/sciadv.aaz1310","volume":"6","author":"Johnson","year":"2020","journal-title":"Sci. Adv."},{"key":"cqgadf0babib28","first-page":"L1","volume":"875","author":"EHT Collaboration","year":"2019","journal-title":"Astrophys. J. Lett."},{"key":"cqgadf0babib29","doi-asserted-by":"publisher","first-page":"12","DOI":"10.3847\/1538-4357\/ac5f54","volume":"930","author":"EHT Collaboration","year":"2022","journal-title":"Astrophys. J. Lett."},{"key":"cqgadf0babib30","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/acd97b","volume":"40","author":"Vagnozzi","year":"2023","journal-title":"Class. Quantum Grav."},{"key":"cqgadf0babib31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.102.124004","volume":"102","author":"Gralla","year":"2020","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib32","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1086\/167623","volume":"342","author":"Mannheim","year":"1989","journal-title":"Astrophys. J."},{"key":"cqgadf0babib33","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1140\/epjc\/s10052-016-3943-x","volume":"76","author":"Ghosh","year":"2016","journal-title":"Eur. Phys. J. C"},{"key":"cqgadf0babib34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.92.044010","volume":"92","author":"Soroushfar","year":"2015","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib35","doi-asserted-by":"publisher","first-page":"1198","DOI":"10.1088\/0264-9381\/20\/6\/310","volume":"20","author":"Kiselev","year":"2003","journal-title":"Class. Quantum Grav."},{"key":"cqgadf0babib36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.105.211303","volume":"105","author":"Grumiller","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"cqgadf0babib36","volume":"106","author":"Grumiller","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"cqgadf0babib37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2021.10.004","volume":"947","author":"Perlick","year":"2022","journal-title":"Phys. Rep."},{"key":"cqgadf0babib38","doi-asserted-by":"publisher","first-page":"664","DOI":"10.1126\/science.aav8137","volume":"365","author":"Do","year":"2019","journal-title":"Science"},{"key":"cqgadf0babib39","first-page":"L17","volume":"930","author":"EHT Collaboration","year":"2022","journal-title":"Astrophys. J. Lett."},{"key":"cqgadf0babib40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.104047","volume":"103","author":"EHT Collaboration","year":"2021","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib41","doi-asserted-by":"publisher","first-page":"174","DOI":"10.3847\/1538-4357\/acb695","volume":"944","author":"Ghosh","year":"2023","journal-title":"Astrophys. J."},{"key":"cqgadf0babib42","doi-asserted-by":"publisher","first-page":"51","DOI":"10.3847\/1538-4357\/ac6dda","volume":"932","author":"Afrin","year":"2022","journal-title":"Astrophys. J."},{"key":"cqgadf0babib43","doi-asserted-by":"publisher","first-page":"149","DOI":"10.3847\/1538-4357\/acb334","volume":"944","author":"Afrin","year":"2023","journal-title":"Astrophys. J."},{"key":"cqgadf0babib44","doi-asserted-by":"publisher","first-page":"5927","DOI":"10.1093\/mnras\/stab1260","volume":"504","author":"Afrin","year":"2021","journal-title":"Not. Roy. Astron. Soc."},{"key":"cqgadf0babib45","doi-asserted-by":"publisher","first-page":"1997","DOI":"10.1007\/s10714-008-0661-1","volume":"40","author":"Arnowitt","year":"2008","journal-title":"Gen. Rel. Gravit."},{"key":"cqgadf0babib46","author":"Xia"},{"key":"cqgadf0babib47","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.94.084015","volume":"94","author":"Ishihara","year":"2016","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib48","doi-asserted-by":"publisher","first-page":"148","DOI":"10.3847\/1538-4357\/ab96c6","volume":"897","author":"Gold","year":"2020","journal-title":"Astrophys. J."},{"key":"cqgadf0babib49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.084055","volume":"108","author":"da Silva","year":"2023","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib50","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.124055","volume":"109","author":"Claros","year":"2024","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib51","doi-asserted-by":"publisher","first-page":"A24","DOI":"10.1051\/0004-6361\/202037471","volume":"640","author":"Poutanen","year":"2020","journal-title":"Astron. Astrophys."},{"key":"cqgadf0babib52","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1063\/1.1308507","volume":"42","author":"Claudel","year":"2001","journal-title":"J. Math. Phys."},{"key":"cqgadf0babib53","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.79.064016","volume":"79","author":"Cardoso","year":"2009","journal-title":"Phys. Rev. D"},{"key":"cqgadf0babib54","author":"Ayzenberg","year":"2023"}],"container-title":["Classical and Quantum Gravity"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T10:07:32Z","timestamp":1753697252000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/adf0ba"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,28]]},"references-count":55,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2025,7,28]]},"published-print":{"date-parts":[[2025,8,1]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6382\/adf0ba","relation":{},"ISSN":["0264-9381","1361-6382"],"issn-type":[{"value":"0264-9381","type":"print"},{"value":"1361-6382","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,28]]},"assertion":[{"value":"Constraints on the \u03b3-parameter for the vacuum solution of Cotton gravity with geodesics and shadows","name":"article_title","label":"Article Title"},{"value":"Classical and Quantum Gravity","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2025 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2024-12-31","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-07-16","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-07-28","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}