The Rotation Curve of the Milky Way: State of the Art, the Keplerian Decline Debate, and Implications for Dark Matter
For four decades, the roughly flat rotation curve (RC) of the Milky Way (MW) stood as local evidence for an extended dark matter (DM) halo. \textit{Gaia} DR3 has changed the picture: several analyses now find a velocity decline beyond R \approx 15\kpc, and the most radical interpretation \citep{jiao2023} claims a nearly Keplerian fall-off (\vc \propto R^{-1/2}) that excludes a flat RC at 3\sigma and implies a total dynamical mass of only \sim 2 \times 10^{11}\Msun---three to five times below pre-\textit{Gaia} estimates. Taken at face value, this would make the MW exceptional among comparable spirals and challenge both \LambdaCDM and MOND. It would also alter predictions for direct-detection experiments, although the local DM density is not fixed by virial mass alone. The Keplerian claim rests on the delicate assumptions of axisymmetric Jeans modelling, while stellar streams, globular clusters, satellite kinematics, and the Local Group timing argument generally favour a substantially heavier halo, and cosmological simulations reveal potentially substantial biases in Jeans-inferred outer RCs. This review offers a self-contained, pedagogical account of the debate: we derive the full formalism from first principles---the Jeans equations, the asymmetric drift correction, the standard DM halo and baryonic mass models, the MOND flat-RC prediction, and the timing argument---present an illustrative phenomenological MCMC fit and a Gaussian Process reconstruction of the RC, and critically assess which features of the decline can be regarded as established and which remain open.