Simulating the scattering of low-frequency Gravitational Waves by compact objects using the finite element method

TL;DR

This paper uses finite element simulations to study how low-frequency gravitational waves scatter off compact objects, revealing significant near-field effects on wave amplitude and phase that impact gravitational wave data analysis.

Contribution

The study introduces a numerical FEM approach to simulate GW scattering by compact objects, highlighting wave effects relevant for low-frequency GW detection.

Findings

Weak scattering when wavelength >> Schwarzschild radius

Large amplitude and phase shifts near the scatterer

Wave effects influence GW data analysis in low-frequency experiments

Abstract

We investigate the wave effects of gravitational waves (GWs) using numerical simulations with the finite element method (FEM) based on the publicly available code {\it deal.ii}. We robustly test our code using a point source monochromatic spherical wave. We examine not only the waveform observed by a local observer but also the global energy conservation of the waves. We find that our numerical results agree very well with the analytical predictions. Based on our code, we study the scattering of GWs by compact objects. Using monochromatic waves as the input source, we find that if the wavelength of GWs is much larger than the Schwarzschild radius of the compact object, the amplitude of the total scattered GWs does not change appreciably due to the strong diffraction effect, for an observer far away from the scatterer. This finding is consistent with the results reported in the literature. However, we also find that, near the scatterer, not only the amplitude of the scattered waves is very large, comparable to that of the incident waves, but also the phase of the GWs changes significantly due to the interference between the scattered and incident waves. As the evolution of the phase of GWs plays a crucial role in the matched filtering technique in extracting GW signals from the noisy background, our findings suggest that wave effects should be taken into account in the data analysis in the future low-frequency GW experiments, if GWs are scattered by nearby compact objects in our local environment.