A Phase Space Diagram for Gravity

TL;DR

This paper explores a phase space diagram for gravity incorporating a critical acceleration and length scale, revealing complex behaviors in astrophysical structures and suggesting gravity may mimic dark matter even at atomic scales.

Contribution

It introduces a second critical length scale in modified gravity theories and analyzes its implications for astrophysical phenomena and atomic-scale gravity behavior.

Findings

Identification of a second critical length scale in gravity.

Complex phenomenology in the (mass, length) plane for structures.

Gravity may mimic dark matter at atomic scales.

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.