Relativistic dynamics and Bondi–Hoyle–Lyttleton accretion onto rotating embedded black-hole models

In this paper, we examine the motion of test particles and relativistic accretion mechanisms within the spacetime of a rotating embedded black hole (BH). The geometric properties of the metric and their dynamical consequences for particle trajectories are systematically studied, with a specific focus on circular orbits together with their existence criteria and stability constraints. The effective potential and the corresponding effective force are constructed to quantify the influence of rotation and embedding parameters on the attractive and repulsive sectors of the gravitational interaction. Closed-form expressions for orbital frequencies as measured by a distant observer are derived, enabling a quantitative analysis of relativistic precession phenomena, including periastron advance and Lense–Thirring precession. Furthermore, we conduct general relativistic hydrodynamic simulations of Bondi–Hoyle–Lyttleton (BHL) accretion onto rotating embedded BHs. Within the framework of the BHL accretion mechanism, the numerical solution of the GRH equations shows that the embedding parameter α systematically modifies the morphology of the shock cone formed around embedded BHs relative to the Kerr case. In particular, increasing α widens the cone opening angle, weakens post-shock compression, and enhances the dynamical variability of the flow. The time-dependent mass accretion rate exhibits larger oscillation amplitudes and long-term variability as α increases, whereas these amplitudes are suppressed by the frame-dragging effect associated with the BH spin. The corresponding PSDs show stronger QPO-like features in the low-frequency regime. These features should be interpreted as numerical frequency-domain signatures of the simulated accretion flow, rather than as direct observational detections, and may provide a basis for future comparison with observed QPO ranges.