On Newtonian singularities in higher derivative gravity models

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.

Added comment about the black hole solutions in Conclusions section. Fits published version, plus some misprints corrected in formulas at the end of Sect. 3