Nonlocal Modification of Newtonian Gravity

TL;DR

This paper explores a nonlocal extension of Newtonian gravity within a teleparallel framework, proposing a nonlinear modification of Poisson's equation that mimics dark matter effects and analyzing its potential solar system implications.

Contribution

It introduces a novel nonlocal and nonlinear generalization of Newtonian gravity based on a scalar kernel in teleparallel gravity, linking nonlocality to dark matter simulation.

Findings

Nonlocal gravity can replicate dark matter effects.

A nonlinear Poisson equation is derived for nonlocal gravity.

Implications for solar system gravity are briefly discussed.

Abstract

The Newtonian regime of a recent nonlocal extension of general relativity (GR) is investigated. Nonlocality is introduced via a scalar "constitutive" kernel in a special case of the translational gauge theory of gravitation, namely, the teleparallel equivalent of GR. In this theory, the nonlocal aspect of gravity simulates dark matter. A nonlocal and nonlinear generalization of Poisson's equation of Newtonian gravitation is presented. The implications of nonlocality for the gravitational physics in the solar system are briefly studied.