Probing rotating Weyl black hole through accretion-flow dynamics from planar spherical injection and frequencies analysis

In this paper, we analyze the dynamics of test particles in the strong gravitational field and the properties of accretion-induced quasi-periodic oscillations (QPOs) arising around a rotating black hole embedded in Weyl conformal gravity, and we compare the obtained results with the corresponding cases around the standard Kerr black hole. Using the Kerr-Weyl spacetime, we first derive the specific energy, angular momentum, effective potential, and stability conditions of equatorial circular orbits. We examine the influence of the Weyl gravity parameters on the horizon location, the innermost stable circular orbit, and the structure of the effective force. Small perturbations around stable circular orbits are introduced to compute the radial, vertical, and azimuthal epicyclic frequencies. This allows us to evaluate the periastron advance and the Lense-Thirring precession. Our analytical results demonstrate that Weyl gravity induces significant deviations in the oscillation frequencies and modifies the resonance conditions. In addition, we investigate the numerical simulation of planar spherical accretion in the equatorial plane and find that Weyl gravity corrections leave clear and systematic dynamical imprints on the evolution of the accretion flow in the strong gravitational field regime. In particular, increasing Weyl corrections makes the radial component of the flow more dominant and suppresses the azimuthal structure, whereas weaker corrections allow frame-dragging-driven angular dynamics to shape the flow, providing complementary support to the analytical test-particle results.

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