Probing Lorentz-violating effects via precession and accretion disk images in a rotating bumblebee spacetime

We investigate kinematic and optical signatures of Lorentz violation in the strong-field region of a rotating bumblebee spacetime generated by a scalar-gradient bumblebee field. For generic nonextremal rotating configurations with $al\mathrm{\ne }0$, the surface $r=r_{+}$ is curvature singular and is therefore modeled phenomenologically as a perfectly absorbing inner boundary in the ray-tracing calculation. By analyzing the spin precession of test gyroscopes and equatorial timelike geodesics, we find that Lorentz violation suppresses the Lense–Thirring precession of static observers, enhances geodetic precession in the static, spherically symmetric limit, and increases the periastron-precession frequency of bound circular orbits. Images of a geometrically thin accretion disk further show that the Lorentz violation has a negligible impact on the critical curve, while shrinking the inner-shadow-like feature associated with the absorbing boundary and enhancing the lensed ring. These results suggest that selected precession observables and exterior imaging features may provide complementary diagnostics of Lorentz-violating effects in strong-field gravity, whereas the central dark feature remains dependent on the adopted inner-boundary prescription.