Symmetries and Kinematics of Spinning Test Particles Orbiting Kerr-Bertotti-Robinson Black Holes

Introduction: The Kerr-Bertotti-Robinson (Kerr-BR) metric describes a rotating black hole immersed in an external uniform magnetic field, which is fundamentally characterized by its axial symmetry. Investigating the kinematic effects of spinning test particles orbiting this type of black hole offers a valid testbed to explore how background spacetime symmetries govern celestial dynamics under external uniform magnetic fields.

Methods: By employing the Mathisson-Papapetrou-Dixon (MPD) equations, we explore the dynamics of precessing orbits and characteristic equatorial orbital configurations. The underlying continuous symmetries of the spacetime enable the construction of conserved energy and total angular momentum for the spinning particles via the corresponding Killing vectors. A precise formulation for the angular frequency is analytically derived directly from the metric to properly encapsulate the spin-gravity coupling.

Results: Our analysis reveals that the external magnetic field significantly alters the topological structure of the effective potential and modifies orbital stability. Crucially, due to the nonspherical nature of the metric symmetry, a distinct breaking of parameter space symmetry is observed between the prograde (ISCOS) and retrograde (ISCOL) innermost stable circular orbits. While an augmented magnetic field necessitates an increased orbital angular momentum for prograde configurations, sufficiently strong fields completely suppress retrograde circular orbits in near-extremal regimes.

Conclusions: These findings uncover the profound impact of external fields and underlying spacetime symmetries on the trajectories of spinning particles. The analysis of these symmetry-preserving and symmetry-breaking dynamics provides valuable theoretical insights into celestial kinematics, offering refined mathematical templates for future horizon-scale observational tests.