Modeling lunar response to gravitational waves using normal-mode approach and tidal forcing

In light of the recent advances in lunar space missions, a great interest into using the Moon as a future environment for gravitational waves (GWs) detectors has been initiated. The Moon offers a unique environment for such detectors due to constrained noise sources, since unlike Earth it does not have oceans and atmosphere. In this paper, we further explore the idea of using the Moon as a giant resonator of GWs, a proposal that was first introduced by Weber in 1969. This idea is relaying on the theory how GWs interact with free masses and finally elastic solids, such as is a planet to some approximation. We start by carefully setting up general relativity (physics) and elastic theory (geophysics) background to be able to derive analytically the coupling between GWs and elastic solids through associated equations of motion. Once the analytical solution is derived, we explore the parameter space this interaction depends on. This eventually provides us with the transfer function, which defines the frequency band of the interest. We show how this interaction robustly depends on the regolith structure by altering the initial lunar model and exploring different regolith models. Our results show that detection might be troublesome in the high frequency regime between 0.1 and 1 Hz, without beforehand constraining the regolith structure with geophysical methods. Finally, we discuss what are the implications of detecting these signals with the future GW detectors build on the Moon.