Relativistic Dynamics and Bondi-Hoyle-Lyttleton Accretion onto Rotating Embedded Black Hole Models

TL;DR

The paper analyzes how embedding corrections in a rotating black-hole spacetime affect both test-particle dynamics and Bondi-Hoyle-Lyttleton accretion. It combines analytic geodesic results—covering circular orbits, the effective potential $V_{eff}$, epicyclic frequencies, and precession frequencies $\,\Omega_P$ and $\Omega_{LT}$—with GRHD simulations to study how the embedding parameter $\alpha$ and spin $a$ reshape orbital binding, frame-dragging, and accretion flow structure. Key findings show that increasing $\alpha$ (i) broadens the shock cone, (ii) weakens post-shock compression, and (iii) enriches the QPO spectrum with more LFQPOs and robust frequency commensurabilities, while also reducing frame-dragging effects. The results, consistent between test-particle dynamics and full GRHD simulations, demonstrate that embedding provides observable spacetime signatures near black holes and offers a framework to test deviations from Kerr geometry with timing and accretion-flow observations.

Abstract

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.

Figures (14)

• Figure 1: Radial behavior of the conserved energy of neutral test particles moving on circular orbits around a rotating and embedded BH. The profiles illustrate the dependence of the particle energy on the spacetime parameters and orbital radius.
• Figure 2: Radial distribution of the conserved angular momentum of neutral test particles orbiting a rotating and embedded BH, showing how the spacetime rotation and embedding parameters modify the angular momentum requirement for stable motion.
• Figure 3: Testing Effective potential for particles around a rotating and embedded BH.
• Figure 4: Effective force acting on particles orbiting a rotating and embedded BH as a function of the radial coordinate $r$.
• Figure 5: Fundamental frequencies of particles moving in the spacetime of a rotating and embedded BH.