{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T17:15:06Z","timestamp":1783444506368,"version":"3.54.6"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T00:00:00Z","timestamp":1661990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Innovative Development of the Republic of Uzbekistan","award":["F-FA-2021-432"],"award-info":[{"award-number":["F-FA-2021-432"]}]},{"name":"Ministry of Innovative Development of the Republic of Uzbekistan","award":["F-FA-2021-510"],"award-info":[{"award-number":["F-FA-2021-510"]}]},{"name":"Ministry of Innovative Development of the Republic of Uzbekistan","award":["MRB-2021-527"],"award-info":[{"award-number":["MRB-2021-527"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Axial symmetry and stationary properties of spacetime allow to find exact analytical solutions of differential equations describing fields and particles in a gravitational background. The present work is mainly devoted to derivation of exact solutions of Maxwell\u2019s equations for magnetic fields generated by current loops around static black holes (BHs) in Einstein-aether gravity based on the spacetime symmetries in both regions: (i) interior and (ii) exterior to the current loop for a proper observer. The spacetime symmetries are applied in separating variables to solve the second order ordinary differential equation for vector potential of electromagnetic field and the equations of motion of test particles around the aether BH. We also study effects of the aether field on innermost stable circular orbits (ISCOs) of the test particles assuming the current loop position is placed there. It is obtained that the ISCO radius, as well as dipole magnetic moment of the current loop decrease with the increase of the aether parameter c14. Moreover, the performed analysis indicates that the aether field causes a decrease in the magnetic field inside and outside the current loop due to the change of its position.<\/jats:p>","DOI":"10.3390\/sym14091809","type":"journal-article","created":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T03:55:38Z","timestamp":1662004538000},"page":"1809","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Electromagnetic Fields around Black Holes in Einstein \u00c6ther Gravity"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9293-1838","authenticated-orcid":false,"given":"Javlon","family":"Rayimbaev","sequence":"first","affiliation":[{"name":"Ulugh Beg Astronomical Institute, Astronomy St. 33, Tashkent 100052, Uzbekistan"},{"name":"College of Engineering, Akfa University, Kichik Halqa Yuli Street 17, Tashkent 100095, Uzbekistan"},{"name":"Power Engineering Faculty, Tashkent State Technical University, Tashkent 100095, Uzbekistan"},{"name":"Faculty of Physics, National University of Uzbekistan, Tashkent 100174, Uzbekistan"},{"name":"Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent 100000, Uzbekistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1232-610X","authenticated-orcid":false,"given":"Bobomurat","family":"Ahmedov","sequence":"additional","affiliation":[{"name":"Ulugh Beg Astronomical Institute, Astronomy St. 33, Tashkent 100052, Uzbekistan"},{"name":"Faculty of Physics, National University of Uzbekistan, Tashkent 100174, Uzbekistan"},{"name":"Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent 100000, Uzbekistan"},{"name":"Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Kori Niyoziy, 39, Tashkent 100000, Uzbekistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eldor","family":"Karimbaev","sequence":"additional","affiliation":[{"name":"Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent 100000, Uzbekistan"},{"name":"Institute of Nuclear Physics, Ulugbek 1, Tashkent 100214, Uzbekistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jacobson, T. 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