General relativistic dynamics of the Milky Way with Gaia DR3 and relativistic effects from cosmological simulations on galaxy scales

The dynamics of galaxies are typically described using Newtonian gravity, yet General Relativity (GR) may introduce non-negligible effects. The μas-precision astrometry from Gaia, analysed within a relativistic framework, motivates a consistent GR modelling of the Milky Way. Based on Gaia DR3 data, the rotation curve of the Galaxy is analysed using a sample of unprecedented homogeneity and scale, made up of 719143 young disc stars within |z| < 1 kpc and from R ≃ 4.5 to 19 kpc. A general relativistic model derived from a dust disc-scale metric is found statistically equivalent to three state-of-the-art dynamical models: a classical one with a Navarro-Frenk-White dark matter halo, a ΛCDMmodel with an Einasto profile, and MOND. All models reproduce the observed stellar kinematics with similar accuracy, with consistent predictions on the baryonic mass. In the GR model, the gravitational dragging accounts for approximately 30–37% of the rotation curve at the Sun’s position, confirming the ansatz of a ‘DMlike’ effect induced by the spacetime geometry. On the other hand, purely GR phenomena are also neglected in the non-linear evolution of structures, where Newtonian N-body simulations are employed. In the post-Friedmann framework, a frame-dragging potential arises at leading order as sourced by energy currents, contributing to the metric even if the dynamics is Newtonian, and can thus be extracted from N-body simulations. Using the IllustrisTNG simulations, its power spectrum is measured down to galactic scales. Although two orders of magnitude larger than predicted by perturbation theory, the frame-dragging remains a 1–0.1% effect compared to the Newtonian potential. This suggests that, within the ΛCDM framework, no significant frame-dragging emerges from the non-linear evolution of cosmic structures, and it is therefore unlikely to affect galaxy rotation. Whether the gravitational dragging inferred from the exquisite Gaia DR3 in the Milky Way reflects a strong-field local phenomenon or a broader relativistic effect remains an important open question, requiring further studies of Einstein’s solutions along with a direct comparison between relativistic galaxy models and high-resolution relativistic simulations with baryonic physics.