A formal framework for a nonlocal generalization of Einstein's theory of gravitation

TL;DR

This paper introduces a nonlocal generalization of Einstein's gravity theory, suggesting it can explain dark matter phenomena as a manifestation of gravity's nonlocality, aligning with astrophysical observations.

Contribution

It develops a formal nonlocal gravity framework based on gauge theory analogies, connecting it to dark matter explanations within Einstein's theory.

Findings

Nonlocal gravity mimics dark matter effects

Equivalent to general relativity with dark matter in linear approximation

Provides a theoretical basis for astrophysical dark matter evidence

Abstract

The analogy between electrodynamics and the translational gauge theory of gravity is employed in this paper to develop an ansatz for a nonlocal generalization of Einstein's theory of gravitation. Working in the linear approximation, we show that the resulting nonlocal theory is equivalent to general relativity with "dark matter". The nature of the predicted "dark matter", which is the manifestation of the nonlocal character of gravity in our model, is briefly discussed. It is demonstrated that this approach can provide a basis for the Tohline-Kuhn treatment of the astrophysical evidence for dark matter.