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 and embedded BH. In this case, 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. Also, 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 BHL accretion onto rotating embedded BHs. In addition, within the framework of the BHL accretion mechanism, the numerical solution of the GRH equations shows that the embedding parameter αsystematically modifies the morphology of the shock cone formed around embedded BHs compared to the Kerr model. In particular, a wider opening angle of the cone is produced, the compression of matter in the post-shock region is weakened, and the dynamical variability of the flow is enhanced. The time-dependent mass accretion rate exhibits increasing oscillation amplitudes and long-term variations with increasing α, while these amplitudes are found to be suppressed by the frame-dragging effect associated with the BH spin parameter. At the same time, increasing values of $α$ lead to a strengthening of the QPO frequencies formed around embedded BHs in the LFQPO regime, enhancing their observability and increasing the likelihood of detecting commensurate frequency ratios such as 3:2.

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