A Phase Space Diagram for Gravity

In modified theories of gravity including a critical acceleration scale a0, a critical length scale rM = (GM/a0) will naturally arise with the transition from the Newtonian to the dark matter mimicking regime occurring for systems larger than rM . This adds a second critical scale to gravity, in addition to the one introduced by the criterion v < c of the Schwarzschild radius, rS = 2GM/c. The distinct dependencies of the two above length scales give rise to non-trivial phenomenology in the (mass, length) plane for astrophysical structures, which we explore here. Surprisingly, extrapolation to atomic scales suggests gravity should be at the dark matter mimicking regime there.