Modified Newtonian Dynamics (MOND)

This chapter presents Modified Newtonian Dynamics (MOND), the proposal that, below a certain acceleration scale $a_0$, dynamics departs from the Newtonian expectation. In that context, the determining factor for the emergence of apparent missing matter in galactic systems is predicted to be the acceleration, and not the mass or size of the system. MOND enables, for example, the prediction of rotation curves from only the baryonic distribution of galaxies. The simple rule is that the acceleration observed in the low-acceleration regime is the square root of the Newtonian expectation times $a_0$. Immediately, the flatness of rotation curves follows, as well as the proportionality of the fourth power of the asymptotic circular speed to only the baryonic mass of the galaxy. While the asymptotic circular speed is predicted not to depend on the baryonic surface density of galaxies of fixed baryonic mass, the inner shape of rotation curves is predicted to strongly depend on it. More generally, MOND implies an algebraic relation between the acceleration expected from Newtonian gravity and the total observed acceleration, at any radius in a galaxy. This is known, observationally, as the Radial Acceleration Relation. For galaxy clusters, it is commonly accepted that MOND fails, needing a stronger gravitational force (or more baryonic mass than observed) to account for the thermodynamic state of galaxy clusters, their lensing and kinematics. MOND, however, is not a complete theory, but a phenomenological non-relativistic paradigm in the limit of low accelerations, in need of embedding in a more fundamental theory. While various non-relativistic field theories of MOND exist, the search for a relativistic theory that recovers general relativity for high accelerations and MOND for low accelerations in the quasi-static limit, as well as a cosmology compatible with observations, is still on-going.