Lorentz violation signatures in the low-energy sector of Ho\v{r}ava gravity from black hole shadow observations

TL;DR

This study uses black hole shadow observations to explore potential Lorentz violation signatures in Hořava gravity, finding that current data could challenge general relativity if certain conditions are met.

Contribution

It introduces a numerical ray-tracing method to analyze black hole shadows in Hořava gravity and constrains Lorentz violation parameters using EHT observations.

Findings

Lorentz violation signatures can be present in black hole shadows.

Constraints on Lorentz violation depend on black hole spin and observational data.

Future observations could challenge general relativity based on spin measurements.

Abstract

In this paper, we use the Ho\v{r}ava 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 Ho\v{r}ava 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 strength. However, for Sgr A*, we can impose certain parameter constraints on Lorentz violation. These constraints depend on the BH's spin. If future observations confirm Sgr A*'s spin parameter less than 0.81 at maximum inclination, current EHT results would challenge general relativity and support Lorentz violation in low-energy regimes.