On the problem of deformed spherical systems in Modified Newtonian Dynamics

TL;DR

This paper investigates the gravitational fields in Modified Newtonian Dynamics (MOND) for slightly non-spherical mass distributions, offering new analytical approaches that simplify understanding MOND's implications without relying heavily on specific interpolation functions.

Contribution

It introduces four analytical approaches to study MONDian gravitational fields for non-spherical systems, including solutions independent of the interpolation function for certain cases.

Findings

Derived solutions for MOND fields in non-spherical geometries.

Identified conditions where solutions are independent of the interpolation function.

Provided a framework for analyzing MOND without full nonlinear Poisson equation complexity.

Abstract

Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which they supposedly determine. This is typically attributed to the existence of dark matter, which possesses mass but does not radiate (or absorb radiation). Alternatively, the mismatch can be explained if the underlying dynamics is not Newtonian. Within this conceptual scheme, Modified Newtonian Dynamics (MOND) is a successful theoretical paradigm. MOND is usually expressed in terms of a nonlinear Poisson equation, which is difficult to analyse for arbitrary matter distributions. We study the MONDian gravitational field generated by slightly non-spherically symmetric mass distributions based on the fact that both Newtonian and MONDian fields are conservative (which we refer to as the compatibility condition). As the non-relativistic version of MOND has two different formulations (AQUAL and QuMOND) and the compatibility condition can be expressed in two ways, there are four approaches to the problem in total. The method involves solving a suitably defined linear deformation potential, which generally depends on the choice of MOND interpolation function. However, for some specific form of the deformation potential, the solution is independent of the interpolation function.