Detecting Lorentz-violation induced by a tensor field with S-star's motion around Sgr A*

Abstract

Testing Lorentz symmetry in strong gravitational fields provides a unique probe of extensions to standard model. The orbiting motions of the S-stars around the supermassive black hole Sgr~A* provide a natural laboratory for such tests. In this paper, we analyze the S2 orbital data focusing on a static and spherically symmetric black hole within Kalb--Ramond gravity, where the deviations from general relativity are encoded in a single Lorentz-violating parameter $\ell$ introduced by the Kalb--Ramond tensor field. Using a full 14-dimensional Markov Chain Monte Carlo analysis under uniform and Gaussian priors, we obtain $\ell ={1.60\times 10^{-5}}_{-1.76\times 10^{-4}}^{+1.38\times 10^{-4}}$ and $\ell ={-1.02\times 10^{-5}}_{-1.19\times 10^{-4}}^{+1.26\times 10^{-4}}$ 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*. We also perform MCMC simulation by fitting data of S38 and S55 stars, as well as their joint analysis. Our results show that the best fit values of $\ell$ in all simulations are always of $10^{-5}$ order, but S2 star provides the most stringent constraints on the parameters because S2 star has higher precision observational data comparing to the fewer public data for other two stars.

Available online 3 June 2026