Gradient modification of Newtonian gravity

TL;DR

This paper introduces a gradient-based extension of Newtonian gravity within gradient field theory, aiming to regularize singularities and explore potential experimental deviations from classical gravity at short distances.

Contribution

It presents a novel second gradient generalization of Newtonian gravity, providing regularization of singularities and connecting to nonlocal and Yukawa-type interactions.

Findings

Regularization of Newtonian singularities

Finite modifications of gravitational potential and force

Potential experimental tests of short-distance gravity deviations

Abstract

A second gradient generalization of Newtonian gravity is presented within the framework of gradient field theory. Weak nonlocality is introduced via first and second gradients of the gravitational field strength in the Lagrangian density. Gradient generalizations of the Poisson equation of Newtonian gravitation for the gravitational potential and of the generalized Gauss law for the gravitational field strength are presented. Such a gradient modification of Newtonian gravity provides a straightforward regularization of Newtonian gravity removing the classical Newtonian singularities. Finite gradient modifications of the gravitational potential energy and of the gravitational force law are constructed, with a possible connection to Yukawa interaction, and as suitable candidates for experimental tests of Newton's inverse-square law at short distances. In addition, nonlocal gravity of exponential type is investigated and its relation to gradient gravity theory is given.