Propagation of gravitational waves in an expanding background in the presence of a point mass

TL;DR

This paper analyzes how gravitational waves propagate in an expanding universe with a point mass, showing that the mass amplifies the wave and causes a frequency decrease due to gravitational time delay.

Contribution

It provides an analytical solution for gravitational wave propagation in a Newtonian McVittie background with a point mass, highlighting the effects of mass on wave amplitude and frequency.

Findings

Point mass increases gravitational wave amplitude.

Point mass decreases wave frequency as observed at infinity.

Wave propagation is affected by the expanding background and local mass presence.

Abstract

We solve the Laplace equation $\Box h_{ij}=0$ 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.