Modified Newtonian Dynamics In Dimensionless Form

TL;DR

This paper reformulates Modified Newtonian Dynamics in a dimensionless framework, analyzing how gravitational modifications depend on mass distribution and scale, and deriving the effective potential for better physical understanding.

Contribution

It introduces a dimensionless formulation of MOND, highlighting scale-dependent modifications and deriving the effective gravitational potential.

Findings

Modification of gravity depends on mass distribution and scale.

Effective potential for the modified gravity is derived.

Separation into short- and long-distance fields aids understanding.

Abstract

Modified Newtonian dynamics proposed that gravitational field needs modifications when the field strength $g$ is weaker than a critical value $g_0$. This has been shown to be a good candidate as an alternative to cosmic dark matter. There is another way to look at this theory as a length scale dependent theory. One will show that modification of the Newtonian field strength depends on the mass distribution and the coordinate scale of the system. It is useful to separate the effective gravitation field $g(r)$ into a small scale (or short-distance)$g_s$ field and a large scale (or a long-distance) $g_l$ field that should be helpful for a better understanding of the underlying physics. The effective potential is also derived.