Propagation of gravitational waves in an expanding background in the presence of a point mass
arXiv:1607.08103 · doi:10.1103/PhysRevD.94.084018
Abstract
We solve the Laplace equation describing the propagation of gravitational waves in an expanding background metric with a power law scale factor in the presence of a point mass in the weak field approximation (Newtonian McVittie background). We use boundary conditions at large distances from the mass corresponding to a standing spherical gravitational wave in an expanding background which is equivalent to a linear combination of an incoming and an outgoing propagating gravitational wave. We compare the solution with the corresponding solution in the absence of the point mass and show that the point mass increases the amplitude of the wave and also decreases its frequency (as observed by an observer at infinity) in accordance with gravitational time delay.
arXiv comment10 pages, 6 figures. The Mathematica files with the numerical analysis of this study may be downloaded from https://drive.google.com/file/d/0B7rg6X3QljQXck5YSmQ5Rl9HeUU/view . Minor modifications compared to previous version (typos and improved presentation). Accepted in Phys. Rev. D. To appear
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