Nonlocal Gravity

TL;DR

This paper develops a nonlocal generalization of Einstein's gravity theory, which effectively mimics dark matter by introducing a scalar kernel, connecting nonlocality with astrophysical dark matter phenomena.

Contribution

It introduces a nonlocal gravity theory using a scalar kernel within teleparallel gravity, providing a new perspective on dark matter as a manifestation of nonlocality.

Findings

Nonlocal gravity can be formulated via a scalar kernel in teleparallel gravity.

The theory reproduces dark matter effects in the linear approximation.

It supports the phenomenological Tohline-Kuhn modified gravity approach.

Abstract

The analysis of measurements of accelerated observers in Minkowski spacetime has led to the development of nonlocal special relativity theory. Inertia and gravitation are intimately connected in accordance with the principle of equivalence. We therefore seek a nonlocal generalization of the theory of gravitation such that in the new theory the field equations are integro-differential equations for the local gravitational field. We show that it is possible to develop a nonlocal generalization of Einstein's theory of gravitation via the introduction of a scalar "constitutive" kernel in the teleparallel equivalent of general relativity. The resulting nonlocal theory is essentially equivalent to Einstein's theory plus "dark matter". That is, nonlocality simulates dark matter by introducing a new source term into general relativity. In the linear approximation for the nonlocal modification of Newtonian gravity, we recover the theoretical basis for the phenomenological Tohline-Kuhn modified gravity approach to the explanation of the astrophysical evidence for dark matter.