Newtonian Counterparts of Spin 2 Massless Discontinuities

TL;DR

This paper investigates the differences in Newtonian limits of massive spin 2 theories and Newtonian cosmology, explaining why certain discontinuities present in relativistic theories do not appear in their Newtonian counterparts.

Contribution

It clarifies the physical reasons behind the absence of discontinuities in Newtonian limits of massive spin 2 theories, contrasting with their presence in Newtonian cosmology.

Findings

Newtonian limits of massive spin 2 theories do not exhibit discontinuities.

Discontinuities in Newtonian cosmology can be removed for finite ranges.

The paper provides a physical explanation for these differences.

Abstract

Massive spin 2 theories in flat or cosmological ($\Lambda \ne 0$) backgrounds are subject to discontinuities as the masses tend to zero. We show and explain physically why their Newtonian limits do not inherit this behaviour. On the other hand, conventional ``Newtonian cosmology'', where $\Lambda $ is a constant source of the potential, displays discontinuities: e.g. for any finite range, $\Lambda$ can be totally removed.