On the cancellation of Newtonian singularities in higher-derivative gravity

TL;DR

This paper demonstrates that higher-derivative gravity theories with complex poles in their propagator produce a finite, non-singular Newtonian potential at the origin, extending previous results to more general cases.

Contribution

It extends the analysis of Newtonian potential regularity to higher-derivative gravity models with complex poles, showing the potential remains finite regardless of pole nature or multiplicity.

Findings

The classical potential is real and regular at the origin.

Explicit expressions for the potential are derived in specific cases.

Regularity can occur even with unequal numbers of tensor and scalar modes.

Abstract

Recently there has been a growing interest in quantum gravity theories with more than four derivatives, including both their quantum and classical aspects. In this work we extend the recent results concerning the non-singularity of the modified Newtonian potential to the most relevant case in which the propagator has complex poles. The model we consider is Einstein-Hilbert action augmented by curvature-squared higher-derivative terms which contain polynomials on the d'Alembert operator. We show that the classical potential of these theories is a real quantity and it is regular at the origin disregard the (complex or real) nature or the multiplicity of the massive poles. The expression for the potential is explicitly derived for some interesting particular cases. Finally, the issue of the mechanism behind the cancellation of the singularity is discussed; specifically we argue that the regularity of the potential can hold even if the number of massive tensor modes and scalar ones is not the same.