Spinning test particle dynamics and near-horizon collisions in a GUP-modified Schwarzschild spacetime

Abstract

The Generalized Uncertainty Principle (GUP), motivated by various approaches to quantum gravity, predicts a fundamental minimal length that manifests as low-energy deformations of classical black hole spacetimes. We investigate the strong-field dynamics of spinning test particles in a spherically symmetric black hole geometry incorporating a GUP correction of strength \(\epsilon\)–the S-GUP metric–using the Mathisson–Papapetrou–Dixon (MPD) formalism with the Tulczyjew spin supplementary condition. We derive the effective potential governing radial motion, establish the conditions for circular orbits, and determine the innermost stable circular-orbit (ISCO) radius, energy, and angular momentum as functions of \(\epsilon\) and the particle’s specific spin s. The superluminal bound, which restricts the spin magnitude to physically admissible timelike trajectories, yields a maximum spin \(s_{\max }(\epsilon )\) that exhibits a non-monotonic behavior: it decreases from the Schwarzschild value to a shallow minimum near \(\epsilon \approx 0.5\)–0.7, then rises sharply as the extremal limit \(\epsilon \rightarrow 1\) is approached. We further compute the center-of-mass energy of head-on collisions between two spinning particles near the horizon, finding that spin misalignment and the GUP correction act constructively to significantly enhance the collision energy. Numerical integration of representative trajectories reveals that negative \(\epsilon\) induces pronounced rosette-like precession, while positive \(\epsilon\) yields more compact, nearly closed orbits. These results demonstrate that GUP-induced quantum corrections and spin–curvature coupling jointly modify the orbital structure, ISCO properties, and collision energetics in ways that are, in principle, distinguishable from classical general-relativistic predictions, thereby establishing spinning test particles as potential probes of minimal-length quantum-gravity effects in astrophysical environments.