Probing Observable Features of Lorentz violation in Low-Energy Ho\v{r}ava Gravity with Accretion Disk Images of Black Hole

Abstract

In this paper, we study the observable signatures of Lorentz violation (LV) in low-energy Horava gravity by simulating the images and polarization features of rotating LV black holes using a backward ray-tracing method. Within a thin-disk accretion model and the ZAMO framework, we numerically solve the geodesics equation of photon and simulate the corresponding thin-disk images and polarization patterns. The results show that the LV parameter l strongly affects the inner shadow, brightness asymmetry, and polarization properties of the thin disk. The decrease of l leads to a more elliptical and untilted inner shadow, while increasing l produces a pronounced leftward D-shaped structure of the critical curve. In addition, the variation of l alters the distribution of polarized intensity and polarization direction, especially near the critical curve. Moreover, it also shows that a positive l enhances the black hole's angular velocity, while a negative one suppresses it, indicating that the sign of l determines the trend direction of the LV effect. These findings suggest that future high-resolution EHT observations combining the thin-disk images and polarization patterns could provide valuable tests of the LV effect.