Eur. Phys. J. C (2025) 85: 800
https://doi.org/10.1140/epjc/s10052-025-14541-y

Regular Article - Theoretical Physics

Dynamics of spinning particles around static black holes in effective quantum gravity

¹ National Research University TIIAME, Kori Niyoziy 39, 100000, Tashkent, Uzbekistan
² Kimyo International University in Tashkent, Shota Rustaveli Str. 156, 100121, Tashkent, Uzbekistan
³ University of Tashkent for Applied Sciences, Str. Gavhar 1, 100149, Tashkent, Uzbekistan
⁴ Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, 1096, Baku, Azerbaijan
⁵ Centre for Theoretical Physics, Jamia Millia Islamia, 110025, New Delhi, India
⁶ Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag 54001, 4000, Durban, South Africa
⁷ New Uzbekistan University, Movarounnahr Street 1, 100000, Tashkent, Uzbekistan
⁸ School of Physics, Harbin Institute of Technology, 150001, Harbin, People’s Republic of China
⁹ Department of Physics, Zhejiang Normal University, 321004, Jinhua, People’s Republic of China
¹⁰ Zhejiang Institute of Photoelectronics and Zhejiang Institute for Advanced Light Source, Zhejiang Normal University, 321004, Jinhua, Zhejiang, People’s Republic of China

^a gmustafa3828@gmail.com

Received: 20 April 2025
Accepted: 14 July 2025
Published online: 24 July 2025

Abstract

We investigate the dynamics of spinning test particles orbiting static black holes in effective quantum gravity (EQG) using the Mathisson–Papapetrou–Dixon (MPD) formalism with two distinct models. The purpose of using two models is to compare qualitatively different realizations of EQG corrections and assess their impact on spin-gravity coupling and orbital behavior. Through analysis of the effective potential, we demonstrate how $\zeta$ and particle spin s jointly influence orbital stability, revealing that (i) in Model-1, increasing $\zeta$ elevates the potential barrier while spin effects become dominant near the horizon, (ii) Model-2 shows weaker dependence on $\zeta$ except for high-spin configurations. The innermost stable circular orbits (ISCOs) exhibit characteristic scaling $r_{\text{ISCO}}(\zeta ,s)$, with quantum corrections that increase the radius of the ISCO by up to 27% relative to Schwarzschild for $\zeta =4$ in Model-1. We derive critical spin values $s_{\text{max}}$ beyond which particle trajectories become spacelike, finding $s_{\text{max}}$ decreases monotonically with $\zeta$ in Model-2 but shows non-monotonic behaviour in Model-1. The particle collision energetics are analyzed, showing that the center-of-mass energies $E_{\text{cm}}$ can be enhanced by spin-parameter tuning, reaching $E_{\text{cm}}/2m\sim 8$ for $(\zeta ,s_1,s_2)=(4,-0.5,0.5)$ near the horizon. Trajectory simulations reveal that quantum corrections in Model-1 induce precession effects absent in Model-2, suggesting observational signatures to distinguish EQG models. Our results establish the combined influence of quantum spacetime structure and spin-curvature coupling on the test particle dynamics, with implications for EQG phenomenology and gravitational wave astronomy.