Spinning particles around Einstein-geometric Proca AdS compact objects

Abstract We investigate the dynamics of spinning test particles in the vicinity of Einstein-geometric Proca (EGP) Anti-de Sitter (AdS) compact objects, which arise from metric-Palatini gravity extended by the antisymmetric part of the affine curvature. Using the Mathisson–Papapetrou–Dixon (MPD) equations with the Tulczyjew spin supplementary condition, we derive the effective potential and analyze the equatorial motion of spinning particles. The influence of the model parameters $$q_{1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>q</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> , $$q_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , and the Proca mass parameter $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> on the innermost stable circular orbits (ISCO), superluminal spin bounds, and orbital stability is systematically explored. Our results show that increasing $$q_{1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>q</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and $$q_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> reduces the ISCO radius, angular momentum, and energy, while spin orientation introduces significant modifications to orbital behavior. We further examine head-on collisions of spinning particles near the horizon and demonstrate how the center-of-mass energy depends on spin and the EGP theory parameters. The study reveals that Einstein-geometric Proca AdS black holes may act as efficient particle accelerators, with distinctive features absent in Schwarzschild or standard AdS backgrounds. These findings provide new insights into the interplay between spin dynamics, modified gravity, and strong-field compact object physics.