The MOND limit from space-time scale invariance

Understand

The MOND limit is shown to follow from a requirement of space-time scale invariance of the equations of motion for nonrelativistic, purely gravitational systems; i.e., invariance of the equations of motion under (t,r) goes to (qt,qr), in the limit a0 goes to infinity.

• It is suggested that this should replace the definition of the MOND limit based on the low-acceleration behavior of a Newtonian-MOND interpolating function.
• In this way, the salient, deep-MOND results--asymptotically flat rotation curves, the mass-rotational-speed relation (baryonic Tully-Fisher relation), the Faber-Jackson relation, etc.--follow from a symmetry principle.
• For example, asymptotic flatness of rotation curves reflects the fact that radii change under scaling, while velocities do not.