The Emergence of Radiation from Gravitational Potential Wells: The Absence of $\omega M$ Effects

TL;DR

This paper analyzes gravitational wave propagation near massive galaxies, demonstrating that expected power suppression effects are not present and clarifying the origin of previously predicted suppression terms.

Contribution

It shows that the predicted power suppression factor does not occur and clarifies the nature of the terms in the galaxy's exterior gravitational field expansion.

Findings

No suppression of radiative power by the factor predicted by Kundu.

Small backscatter of order M/ω²R³ occurs during wave propagation.

The expansion terms are not related to source strength or radiation intensity.

Abstract

We consider a source of gravitational waves of frequency $\omega$, located near the center of a massive galaxy of mass $M$ and radius $R$, with $\omega\gg R^{-1}$. In the case of a perfect fluid galaxy, and of odd-parity waves, there is no direct matter-wave interaction and the propagation of the waves is affected by the galaxy only through the curvature of the spacetime background through which the waves propagate. We find that, in addition to the expected redshift of the radiation emerging from the galaxy, there is a small amount of backscatter, of order $M/\omega^2R^3$. We show that there is no suppression of radiative power by the factor $1+\omega^2M^2/4$ as has been recently predicted by Kundu. The origin of Kundu's suppression lies in the interpretation of a term in the expansion of the exterior field of the galaxy in inverse powers of radius. It is shown why that term is not related to the source strength or to the strength of the emerging radiation.