{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T02:03:45Z","timestamp":1783130625860,"version":"3.54.6"},"reference-count":45,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,19]],"date-time":"2023-11-19T00:00:00Z","timestamp":1700352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The study of electromagnetic interactions among test particles with electric charges and magnetic dipole moments is of great significance when examining the dynamics of particles within strong gravitational fields surrounding black holes. In this work, we focus on investigating the dynamics of particles possessing both electric charges and magnetic dipole moments in the spacetime of a Schwarzschild black hole within the framework of modified gravity (MOG), denoted as a Schwarzschild-MOG black hole. Our approach begins by offering a solution to Maxwell\u2019s equations for the angular component of the electromagnetic four potentials within Schwarzschild-MOG spacetime. Subsequently, we derive the equations of motion and establish the effective potential for particles engaged in circular motion. This is achieved using a hybrid formulation of the Hamilton\u2013Jacobi equation, encompassing interactions between electric charges and magnetic dipole moments, the external magnetic field (assumed to be asymptotically uniform), and interactions between the particles and the MOG field. Furthermore, we investigate the impacts of these three types of interactions on critical parameters, including the radius of innermost stable circular orbits (ISCOs), as well as the energy and angular momentum of particles when situated at their respective ISCOs. Finally, a detailed analysis concerning the effects of these interactions on the center-of-mass energy is presented in collisions involving neutral, electrically charged, and magnetized particles.<\/jats:p>","DOI":"10.3390\/sym15112084","type":"journal-article","created":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T00:30:50Z","timestamp":1700440250000},"page":"2084","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Dynamics of Particles with Electric Charge and Magnetic Dipole Moment near Schwarzschild-MOG Black Hole"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2360-4475","authenticated-orcid":false,"given":"Sardor","family":"Murodov","sequence":"first","affiliation":[{"name":"Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent 100000, Uzbekistan"},{"name":"Uzbekistan-Finland Pedagogical Institute, Spitamen Shokh Str. 166, Samarkand 140100, Uzbekistan"},{"name":"Department of Theoretical Physics, Samarkand State University, Samarkand 140104, Uzbekistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9293-1838","authenticated-orcid":false,"given":"Javlon","family":"Rayimbaev","sequence":"additional","affiliation":[{"name":"School of Mathematics and Natural Sciences, New Uzbekistan University, Mustaqillik Ave. 54, Tashkent 100007, Uzbekistan"},{"name":"School of Engineering, Central Asian University, Tashkent 111221, Uzbekistan"},{"name":"Faculty of Computer Engineering, University of Tashkent for Applied Sciences, Gavhar Str. 1, Tashkent 100149, Uzbekistan"},{"name":"Power Engineering Faculty, Tashkent State Technical University, Tashkent 100095, 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":"Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, Tashkent 100000, Uzbekistan"},{"name":"Institute of Theoretical Physics, National University of Uzbekistan, Tashkent 100174, Uzbekistan"},{"name":"Ulugh Beg Astronomical Institute, Astronomy Str. 33, Tashkent 100052, Uzbekistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdullo","family":"Hakimov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Samarkand International University of Technology, 270 Spitamen Avenue, Samarkand 140100, Uzbekistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1038\/458587a","article-title":"Cosmology: Dark matter and dark energy","volume":"458","author":"Caldwell","year":"2009","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"131301","DOI":"10.1103\/PhysRevLett.106.131301","article-title":"Results from a Search for Light-Mass Dark Matter with a P-type Point Contact Germanium Detector","volume":"106","author":"Aalseth","year":"2011","journal-title":"Phys. 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