https://doi.org/10.1140/epjp/s13360-026-07875-3
Regular Article
Spinning particles as probes of quartic square-root Horndeski gravity: spin–curvature coupling and orbital dynamics
1
New Uzbekistan University, Movarounnahr str. 1, 100000, Tashkent, Uzbekistan
2
Institute of Fundamental and Applied Research, National Research University TIIAME, Kori Niyoziy 39, 100000, Tashkent, Uzbekistan
3
Kimyo International University in Tashkent, Shota Rustaveli str. 156, 100121, Tashkent, Uzbekistan
4
Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, AZ1096, Baku, Azerbaijan
5
School of Physics, Harbin Institute of Technology, 150001, Harbin, People’s Republic of China
6
University of Tashkent for Applied Sciences, Str. Gavhar 1, 100149, Tashkent, Uzbekistan
7
Andijan State University, Universitet Str. 129, 170100, Andijan, Uzbekistan
8
Department of Physics, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
9
Department of Physics, School of Science, Aristotle University of Thessaloniki, 541 24, Thessaloniki, Greece
10
S.M. Nikolskii Mathematical Institute of the Peoples’ Friendship University of Russia (RUDN University), 117198, Moscow, Russia
a
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Received:
24
April
2026
Accepted:
23
May
2026
Published online:
2
June
2026
Abstract
We study the equatorial motion of spinning test particles around a static quartic square-root Horndeski black hole within the Mathisson–Papapetrou–Dixon formalism supplemented by the Tulczyjew spin supplementary condition. We derive the spin-dependent effective potential and investigate the timelike-motion constraint through the superluminal bound, which determines the physically admissible spin range of the particle. We then analyze how the Horndeski parameters and the particle spin affect the innermost stable circular orbit (ISCO) and representative bound trajectories. The key aspect of the present analysis is that the spin–curvature coupling is evaluated in a scalar–tensor geometry generated by the quartic square-root Horndeski sector, allowing us to separate spin-induced corrections from deviations associated with the background Horndeski parameters. We show that spin–curvature coupling produces controlled non-geodesic corrections to the motion: the effective potential, allowed spin domain, and ISCO characteristics depend on both the magnitude and sign of the spin. The trajectory results are interpreted as modified orbital behavior, including shifts of radial turning points and changes in orbital compactness, rather than as fundamentally new dynamical regimes. Our results show that spinning-particle dynamics provides a useful probe of strong-field orbital properties in quartic square-root Horndeski black hole space-times.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
