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 $q_{1}$, $q_{2}$, and the Proca mass parameter $σ$ on the innermost stable circular orbits (ISCO), superluminal spin bounds, and orbital stability is systematically explored. Our results show that increasing $q_{1}$ and $q_{2}$ 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.

Figures (7)

• Figure 1: Killing horizon (solid) and event horizon (dashed) for various values of the charge parameter $q_1$ and for fixed $q_2$ as a function of $\sigma$.
• Figure 2: Radial dependence of the effective potential for different values of parameters. The upper line corresponds to the plots of the effective potential for various values of $q_1$ when $q_2=0.5$ (left panel) and for various values of $q_2$ when $q_1=1.0$ (right panel) for $s=0.5$ and $\sigma=0.8$. While the lower line illustrates the behavior of $V_{eff}$ for various values of $s$ for $q_1=1.0$ and $q_2=0.5$ (left panel) and for various values of $\sigma$ for $q_1,q_2,s=0.5$ (right panel)
• Figure 3: The variation of the radius, specific angular momentum, and energy at ISCO in spin $s$ for different values of $q_1$ at fixed $q_2=0.5$ and $\sigma=0.8$, respectively. Here, straight colorful lines in the graph define the superluminal boundary of the particle's spin for each value of the $q_1$, respectively. The left side of the lines corresponds to the time-like particles, while the right side - space-like particles.
• Figure 4: The variation of the radius, specific angular momentum, and energy at ISCO with respect to spin $s$ for various values of $q_2$ and for $q_1=1.0$ and $\sigma=0.8$. The vertical colorful lines define the superluminal constraint on the spin for each value of $q_2$ in the graph.
• Figure 5: The dependence of the critical values of spin $s_{max}$ on parameter $q_1$ for various values of $q_2$ (left panel) and on parameter $q_2$ for various values of $q_1$ (right panel) for $\sigma=0.8$.