Screening and Antiscreening of the MOND field in Perturbed Spherical Systems

TL;DR

This paper investigates how perturbations in spherical systems under MOND are screened or amplified, revealing that the gravitational field inside such systems can be significantly reduced or enhanced depending on the configuration and mass distribution.

Contribution

It demonstrates the screening effect of spherical symmetry on perturbations in MOND systems and explores conditions leading to field amplification, extending understanding of external field effects.

Findings

Perturbed fields inside shells are significantly screened by spherical symmetry.

Inner shell perturbations can be amplified if the inner shell is very light.

Field amplification can reach nearly twice the naive expectation.

Abstract

In the context of Modified Newtonian Dynamics (MOND), we study how perturbation of a spherically symmetric system would affect the gravitational field. In particular, we study systems of perturbed and unperturbed spherical shells. For a single perturbed shell, we show that the field inside the shell is much smaller than what would be expected from a naive scaling formula. The strength of the perturbation field within the shell is screened by the spherically symmetric component of the mass, and is reduced as the spherically symmetric component is increased. For a two-shell system, we again show that the perturbed field is screened by the shells, no matter which shell's mass distribution is perturbed. The field within the inner shell is most suppressed when the inner and outer shells coincide. However, for a very light inner shell, the perturbation to the field can be enhanced. The enhancement is typically larger for smaller inner shells, and the perturbed field can be amplified by almost a factor of 2. The relevance to the effect of external fields on galaxy dynamics is discussed.