Probing a Lorentz-violating parameter from orbital precession of the S2 star around the galactic centre supermassive black hole

Abstract

Testing Lorentz symmetry in strong gravitational fields provides a promising probe of extensions to general relativity. The supermassive black hole Sgr~A* and the orbit of the S-stars offer a laboratory for such tests in a regime beyond weak field limit. We analyze the S2 orbital data focusing on the Schwarzschild-like black hole within bumblebee gravity, where deviations from general relativity are encoded in a single Lorentz-violating parameter $\ell$. Using a full 14-dimensional Markov Chain Monte Carlo analysis under uniform and Gaussian priors, we obtain $\ell ={-8.01\times 10^{-5}}_{-2.09\times 10^{-4}}^{+2.77\times 10^{-4}}$ and $\ell ={1.00\times 10^{-5}}_{-2.91\times 10^{-4}}^{+2.90\times 10^{-4}}$ at $1\sigma$ confidence level, respectively. These constraints are about three orders of magnitude tighter than those from Event Horizon Telescope imaging of Sgr~A*.

16 pages,5 figures

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