PPN–spin degeneracies in mock S62-like stellar-orbit inference

Abstract We investigate the degeneracies between black hole (BH) spin effects and parametrized post-Newtonian (PPN) parameters in the relativistic orbital dynamics of S2-like and S62-like stars orbiting Sagittarius A*. Using a 1PN+SO Hamiltonian framework and synthetic astrometric and radial velocity datasets, we perform Bayesian parameter inference. For current baseline observational precisions, the dominant relativistic observable—the Schwarzschild periapsis advance—allows the recovery of the effective precession parameter ϒ, while leaving the individual PPN parameters γ and β degenerate. Assuming microarcsecond-level astrometric precision, the spin-induced Lense–Thirring signal becomes partially detectable; fixing the PPN sector to General Relativity allows the BH spin magnitude to be constrained to an uncertainty of ~10−2. However, simultaneously varying PPN and spin parameters reveals a strong, approximately linear covariance between ϒ and the dimensionless spin parameter χ. To overcome this limitation, we demonstrate that joint multi-star inference can disentangle the degeneracy by combining a wider-orbit star, which constrains the dominant 1PN sector, with a compact relativistic orbit that is sensitive to Lense–Thirring frame dragging.