Nonlocal Gravity: The General Linear Approximation

TL;DR

This paper develops a linear approximation of nonlocal gravity, showing it can mimic dark matter effects and analyzing light deflection, with potential astrophysical implications.

Contribution

It introduces a general linear approximation of nonlocal gravity within general relativity, deriving field equations and exploring their solutions.

Findings

Nonlocal gravity can simulate dark matter effects in the linear regime.

Light deflection in nonlocal gravity aligns with gravitational lensing observations.

The characteristic length scale of nonlocality is about 1 kpc.

Abstract

The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field equations is derived. The linear approximation of nonlocal gravity (NLG) is thoroughly examined and the solutions of the corresponding field equations are discussed. It is shown that nonlocality, with a characteristic length scale of order 1 kpc, simulates dark matter in the linear regime while preserving causality. Light deflection in linearized nonlocal gravity is studied in connection with gravitational lensing; in particular, the propagation of light in the weak gravitational field of a uniformly moving source is investigated. The astrophysical implications of the results are briefly mentioned.