A Phase Space Diagram for Gravity

Abstract

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.

9 pages, 1 figure, Final version accepted for publication in Entropy

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Cited by in corpus (3)

• Gravitational lensing with $f(\chi )={\chi }^{3/2}$ gravity in accordance with astrophysical observations
• Multidimensional representation of semantic relations between physical theories, fundamental constants and units of measurement with formal concept analysis
• Modified Newtonian dynamics and hadronic scales