Potential-density pairs for axisymmetric galaxies: the influence of scalar fields

TL;DR

This paper develops a new method to model axisymmetric galaxies using scalar-tensor gravity theories, incorporating scalar fields into potential-density pairs and analyzing their effects on galactic rotation curves.

Contribution

It introduces a formulation for potential-density pairs in scalar-tensor gravity, including solutions for axisymmetric systems and their application to galactic disks.

Findings

Derived general solutions for axisymmetric potential-density pairs.

Computed rotation curves for galactic disks with exponential profiles.

Analyzed the influence of scalar fields on gravitational forces.

Abstract

We present a formulation for potential-density pairs to describe axisymmetric galaxies in the Newtonian limit of scalar-tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential-density pairs of galactic disks for an exponential profile and their rotation curves.