A phase space diagram for gravity (Q406068)

Summary: 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 Schwarzschild 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.