A Phase Space Diagram for Gravity
  In modified theories of gravity including a critical acceleration scale,
$a_{0}$, a critical length scale, $r_{M}=(GM/a_{0})^{1/2}$, will naturally
arise, with the transition from the Newtonian to the dark matter mimicking
regime occurring for systems larger than $r_{M}$. This adds a second critical
scale to gravity, in addition to the one introduced by the criterion $v < c$ of
the Shwarzschild radius, $r_{S}=2GM/c^{2}$. 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.
