On the Kuzmin model in fractional Newtonian gravity

TL;DR

This paper explores the Kuzmin disk within fractional Newtonian gravity, deriving potential representations and analyzing asymptotic behavior to understand its implications as an alternative to dark matter.

Contribution

It introduces a detailed analysis of the Kuzmin disk in fractional Newtonian gravity, including new potential representations and asymptotic analysis.

Findings

Derived integral and series representations of the potential

Verified asymptotic behavior at large scales

Provided visualizations of equipotential surfaces

Abstract

Fractional Newtonian gravity, based on the fractional generalization of Poisson's equation for Newtonian gravity, is a novel approach to Galactic dynamics aimed at providing an alternative to the dark matter paradigm through a non-local modification of Newton's theory. We provide an in-depth discussion of the gravitational potential for the Kuzmin disk within this new approach. Specifically, we derive an integral and a series representation for the potential, we verify its asymptotic behavior at large scales, and we provide illuminating plots of the resulting equipotential surfaces.