Linearized Gravitational Waves in Nonlocal General Relativity

TL;DR

This paper studies gravitational waves in a nonlocal extension of general relativity, finding that deviations from Einstein's theory are negligible at frequencies above 10^{-8} Hz, relevant for current observations.

Contribution

It introduces an analysis of gravitational radiation within nonlocal gravity, showing that nonlocal effects are insignificant at observable high frequencies.

Findings

Nonlocal gravity can mimic dark matter effects in galaxy rotation curves.

Deviations from general relativity are negligible for gravitational waves with frequencies > 10^{-8} Hz.

Nonlocal effects become relevant only at extremely low frequencies (~10^{-12} Hz).

Abstract

We investigate gravitational radiation in the linear approximation within the framework of the recent nonlocal generalization of Einstein's theory of gravitation. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline-Kuhn approach to modified gravity. To account for the observational data regarding the rotation curves of spiral galaxies, nonlocality is associated with a characteristic length scale of order \lambda_0 = 10 kpc. It follows that in nonlocal gravity, the treatment of extremely low-frequency (~ 10^{-12} Hz) gravitational waves with wavelengths of order \lambda_0 would be quite different than in general relativity. However, for radiation of frequency > 10^{-8} Hz, which is the frequency range that is the focus of current observational searches, the corresponding wavelengths are very small compared to \lambda_0. We find that in this frequency regime the nonlocal deviations from general relativity essentially average out and can be safely neglected in practice.