Spin–curvature coupling and spinning particle motion in deformed Schwarzschild spacetime

We investigate the motion of spinning test particles in a deformed Schwarzschild spacetime characterized by two additional parameters, α and β, and governed by the Mathisson–Papapetrou–Dixon equations with the supplementary condition of the Tulczyjew spin. We derive closed-form expressions for conserved quantities, radial momentum, and factorized effective potentials V_eff^± for equatorial motion. A systematic scan of (α,β,s) shows that increasing the specific spin of the particle (co-rotating) s pushes ISCO inward, lowers E_ISCO, and increases L_ISCO; increasing α similarly shifts ISCO inward and decreases all three characteristics of ISCO, while increasing β shifts ISCO outward and increases them. We outline the physical (timelike) domain by enforcing a superluminal bound and extract the critical spin s_max, which decreases mildly with α and increases with β over the explored ranges. We find that the center-of-mass energy of near-horizon head-on collisions is maximum for oppositely oriented spins, and we present trajectory integrations illustrating how larger α and β widen orbital apocenters for fixed initial data. Together, these results chart how spacetime deformations and spin–curvature coupling imprint on orbital structure and high-energy collisions in the strong-gravity regime.