On Newtonian singularities in higher derivative gravity models

TL;DR

This paper investigates how higher derivative gravity models can eliminate Newtonian singularities, showing that in local theories with real simple poles, singularities are canceled by contributions from massive modes.

Contribution

It demonstrates that all local higher-derivative gravity theories with real simple poles naturally remove Newtonian singularities through mode cancellations.

Findings

Singularities are canceled in theories with real simple poles.

Higher derivative models can be made singularity-free.

Cancellation involves scalar and tensor massive modes.

Abstract

We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and super-renormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higher-derivative theories, when the poles of the propagator are real and simple, the singularities disappear due to the cancellation of contributions from scalar and tensor massive modes.