Probing Lorentz-violating effects via precession and accretion disk images of a rotating bumblebee black hole

Abstract

We investigate kinematic and optical signatures of Lorentz-violation in the strong-field region of a rotating bumblebee black hole generated by a scalar-gradient bumblebee field. Through the analysis of spin precession of test gyroscopes and timelike geodesic motion in the spacetime, we find that Lorentz-violating effect suppresses the Lense-Thirring precession near the horizon, while enhancing geodetic precession in the static, spherically symmetric limit. For bound circular orbits in the equatorial plane, the Lorentz-violation leads to an increase in the periastron precession frequency. Furthermore, images of a geometrically thin accretion disk reveal that the Lorentz-violation has a negligible impact on the critical curve, but significantly shrinks the inner shadow and enhances the lensed ring. These results indicate that inner shadow measurements, combined with selected precession observables, may provide complementary probes of Lorentz-violating effects in strong-field gravity.

Figures (11)

• Figure 1: The variation of the periastron precession frequency $\Omega_\text{pre}$ with $r$ for different $l$ and $a$, the vertical lines indicate the location of the ISCO.
• Figure 2: The spin precession frequency as a function of radial coordinate for the rotating bumblebee black hole. In the top row, we adopt different values of parameter $k$ and focus on the influence of the angle $\theta$ on the precession frequency. In the bottom row, we concentrate on the effect of the Lorentz-violating parameter $l$ and spin parameters $a$ on the precession frequency.
• Figure 3: LT precession frequency of a test gyroscope as a function of the radial coordinate $r$ in the rotating bumblebee black hole spacetime.
• Figure 4: The geodetic precession as a function of radial coordinate $r$ for the spherically symmetric bumblebee black hole.
• Figure 5: Imaging results at an observational inclination angle $\theta_o=17^\circ$. Top two rows: Images of a rotating bumblebee black hole illuminated by a geometrically thin accretion disk. The white dashed line indicates the boundary of the inner shadow, and the blue dashed line represents the critical curve. The horizontal and vertical coordinates are in units of $\mu$as. Bottom two rows: Intensity profiles along the $x$ and $y$‑axes for different parameter sets. The horizontal coordinate is in $\mu$as, and the vertical coordinate has been normalized to the peak intensity $I_0$ for each spin case.