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

Abstract

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 $al\neq0$, 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.