Linearized Gravitational Waves in Nonlocal General Relativity

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.