As detections of gravitational waves (GWs) mount, the need to investigate various effects on the propagation of these waves from the time of emission until detection also grows. We investigate how a thin low density dust shell surrounding a gravitational wave source affects the propagation of GWs. The Bondi-Sachs (BS) formalism for the Einstein equations is used for the problem of a gravitational wave (GW) source surrounded by a spherical dust shell. Using linearised perturbation theory, we and the geometry of the regions exterior to, interior to and within the shell. We and that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. This finding is novel. In the context of cosmology, apart from the gravitational redshift, the effects are too small to be measurable; but the effect would be measurable if a GW event were to occur with a source surrounded by a massive shell and with the radius of the shell and the wavelength of the GWs of the same order. We extended our investigation to astrophysical scenarios such as binary black hole (BBH) mergers, binary neutron star (BNS) mergers, and core collapse supernovae (CCSNe). In these scenarios, instead of a monochromatic GW source, as we used in our initial investigation, we consider burst-like GW sources. The thin density shell approach is modified to include thick shells by considering concentric thin shells and integrating. Solutions are then found for these burst-like GW sources using Fourier transforms. We show that GW echoes that are claimed to be present in the Laser Interferometer Gravitational-Wave Observatory (LIGO) data of certain events, could not have been caused by a matter shell. We do and, however, that matter shells surrounding BBH mergers, BNS mergers, and CCSNe could make modifications of order a few percent to a GW signal. These modifications are expected to be measurable in GW data with current detectors if the event is close enough and at a detectable frequency; or in future detectors with increased frequency range and amplitude sensitivity. Substantial use is made of computer algebra in these investigations. In setting the scene for our investigations, we trace the evolution of general relativity (GR) from Einstein's postulation in 1915 to vindication of his theory with the confirmation of the existence of GWs a century later. We discuss the implications of our results to current and future considerations. Calculations of GWs, both analytical and numerical, have normally assumed their propagation from source to a detector on Earth in a vacuum spacetime, and so discounted the effect of intervening matter. As we enter an era of precision GW measurements, it becomes important to quantify any effects due to propagation of GWs through a non-vacuum spacetime Observational confirmation of the modification effect that we and in astrophysical scenarios involving black holes (BHs), neutron stars (NSs) and CCSNe, would also enhance our understanding of the details of the physics of these bodies.
Cylindrical Gravitational Wave: Source and Resonance