The Newtonian limit of fourth and higher order gravity

TL;DR

This paper investigates the Newtonian limit of higher-order gravity theories, revealing that the gravitational potential combines Newtonian and Yukawa terms and is unbounded near the origin.

Contribution

It provides explicit calculations of the gravitational potential for sixth-order gravity and generalizes the behavior of potentials in higher-order gravity theories.

Findings

Potential includes Newtonian and Yukawa components

Potential is unbounded near the origin

Explicit coefficients for sixth-order gravity are derived

Abstract

We consider the Newtonian limit of the theory based on the Lagrangian L = R + \sum a_k R \Box^k R. The gravitational potential of a point mass turns out to be a combination of Newtonian and Yukawa terms. For sixth-order gravity the coefficients are calculated explicitly. For the general case one gets as a result: The the potential is always unbounded near the origin.