Effective delta sources and regularity in higher-derivative and ghost-free gravity

TL;DR

This paper demonstrates that higher-derivative polynomial gravity theories and certain non-local ghost-free models can regularize delta sources, leading to singularity-free weak-field and Newtonian limits, enhancing the understanding of gravity's behavior at small scales.

Contribution

It proves that higher derivatives in gravity theories regularize delta sources and extends this result to non-local ghost-free models, ensuring regular weak-field limits.

Findings

Higher-derivative theories regularize delta sources

Non-local ghost-free gravities have regular Newtonian limits

The approach applies to weakly non-local models

Abstract

It is shown that polynomial gravity theories with more than four derivatives in each scalar and tensor sectors have a regular weak-field limit, without curvature singularities. This is achieved by proving that in these models the effect of the higher derivatives can be regarded as a complete regularization of the delta-source. We also show how this result implies that a wide class of non-local ghost-free gravities have a regular Newtonian limit too, and discuss the applicability of this approach to the case of weakly non-local models.