Lorentz violation signatures in the low-energy sector of Hořava gravity from black hole shadow observations

In this paper, we use the Hořava gravity model and EHT observations of supermassive black holes (BHs) to investigate signatures of Lorentz violation in real astrophysical environments. The Lorentz violation in the rotating Hořava BH spacetime are confined to the strong gravitational field region, being induced by the BH’s rotation. Due to the non-separability of the photon motion equations in this spacetime, we employed a numerical backward ray-tracing method to generate shadow images for various BH parameters. Subsequently, we extracted coordinate positions characterizing the shadow shape from high-pixel images to evaluate the parameter space of the BH. When evaluating M87*, Lorentz violation can occur with arbitrary magnitude. However, for Sgr A*, we can impose certain parameter constraints on Lorentz violation. These constraints depend on the BH’s spin. Should future observations at the highest inclination angle of the spin axis determine that the spin parameter of Sgr A* is less than 0.6, general relativity would be challenged, and the current EHT observations will serve as crucial evidence for the existence of Lorentz violation in low-energy environments.