Spinning particle dynamics around a black hole in Lorentz Gauge theory

In this paper, we explore the motion of spinning test particles in the gravitational field of a black hole within the framework of Lorentz Gauge theory. We begin by analyzing the dynamics of spinning particles using the Mathisson-Papapetrou-Dixon (MPD) equations. The effective potential is then derived and studied as a function of the spacetime parameter A0, also known as the connection constant of the black hole in Lorentz Gauge theory. Subsequently, we investigate the radial energy and angular momentum associated with circular orbits of spinning particles, focusing on the interplay between the parameter A0 and the particle's spin parameter s. Key aspects such as the influence of spin on the innermost stable circular orbit (ISCO), specific angular momentum, and energy at the ISCO are analyzed for various A0 values. Critical spin values smax, beyond which time-like particles transition to space-like and become non-physical, are determined, and their dependence on A0 and the ISCO radius (rISCO) is discussed. Additionally, we examine the center-of-mass energy resulting from the collision of two spinning particles near the black hole's horizon, highlighting the role of spin and spacetime parameters. Finally, we investigate the trajectories of spinning particles in this black hole spacetime, providing a comprehensive analysis of their dynamics in Lorentz Gauge theory.