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

TL;DR

This paper tests Lorentz symmetry near a supermassive black hole using S2 star orbit data, constraining a Lorentz-violating parameter in bumblebee gravity more tightly than previous methods.

Contribution

It provides the first orbital analysis of S2 star data to constrain Lorentz violation in strong gravity regimes with a comprehensive MCMC approach.

Findings

Constraints on Lorentz-violating parameter are about three orders of magnitude tighter than previous bounds.

The analysis yields specific bounds on the parameter  within a 11 confidence level.

The study demonstrates the potential of stellar orbit data to test fundamental physics beyond general relativity.

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}}^{+2.77 \times 10^{-4}}_{-2.09 \times 10^{-4}} $ and $\ell = {1.00 \times 10^{-5}}^{+2.90 \times 10^{-4}}_{-2.91 \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*.