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 star’s 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 ℓ. 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 1σ confidence level, respectively. The results show that, with supermassive Sgr A* black hole as gravity source, the constraints on the Lorentz-violating parameter in the current model in our analysis can be tighter than those from Event Horizon Telescope imaging of Sgr A* as well as the pulsar-Sgr A* systems.