Newtonian Gravity and Galaxy Rotation Curves: An Axisymmetric Green's Function Perspective

TL;DR

This paper explores an alternative to dark matter for explaining galaxy rotation curves, proposing an axially symmetric vortex mass distribution within Newtonian gravity as a potential explanation.

Contribution

It introduces a novel model of galaxy mass distribution using an axisymmetric vortex, offering a new perspective on galaxy rotation without dark matter.

Findings

Identifies properties of vortex mass distributions consistent with observed rotation curves

Suggests potential of vortex models to explain galaxy dynamics

Provides a theoretical framework for alternative gravity-based explanations

Abstract

The standard proposal within the context of General relativity and its weak field Newtonian limit for the nature of dark matter is that it consists of dark matter particles of unknown type. In the present work and specifically for spiral galaxy rotation curves, an alternative possibility is explored, in the form of an axially symmetric vortex mass distribution of finite extent threading the centre of the galaxy and perpendicular to its disk. Some general considerations are developed and characteristic properties are identified, pointing to the potential interest of such an alternative to be studied in earnest.