Multi-orbit S-star probes of Lorentz violation at the Galactic Center

Abstract

We investigate the potential of Galactic-center S-star observations to probe Lorentz violation in the minimal pure-gravity Standard-Model Extension (SME), focusing on parameter degeneracies associated with anisotropic orbital signatures. We construct simulated astrometric and spectroscopic observations of S2 and S55 using fiducial orbital and Galactic-center parameters based on the multi-star solution from the GRAVITY Collaboration and evolve the stellar trajectories using the leading Lorentz-violating two-body dynamics supplemented by the Schwarzschild first-post-Newtonian (1PN) correction. Separate Fisher-matrix analyses of S2 and S55 each resolve seven of the eight independent SME directions, while their joint analysis resolves all eight directions by combining complementary projections from the differently oriented orbits. A subsequent Markov chain Monte Carlo (MCMC) analysis confirms the Fisher forecasts and reaches characteristic 95% credible-level sensitivities of approximately 10^(-3)-10^(-2) for the time-space components and 10^(-5)-10^(-4) for the spatial components. Our results demonstrate that combining S-stars with different orbital orientations is effective for breaking geometrical degeneracies and probing the tensor structure of Lorentz violation in the Galactic-center gravitational field.