Date of Award
Doctor of Philosophy
Alan G Wiseman
John L Friedman, Xavier Siemens, Philip Chang, Patrick Brady
The recent direct observations of gravitational waves by the LIGO-Virgo collaboration [1-6] have been important pieces of evidence in agreement with Einstein's theory of gravity, the General Theory of Relativity. In addition, they open an era of gravitational wave astronomy that promises to give us much more information on the systems that produce gravitational radiation. Perhaps most prominent among these are binary systems composed of either two black holes, two neutron stars, or one black hole and one neutron star. This dissertation details theoretical predictions regarding such systems.
It is hoped that gravitational radiation emanating from binary systems that include at least one neutron star will allow us to determine the equation of state of matter at very high densities, and therefore information on the composition of such matter. We place a theoretical upper limit on the tidal deformability of neutron stars, which describes how easily the shape of neutron stars change in response to an external gravitational field. This upper limit exists because of causality: the sound speed inside a neutron star must be less than the speed of light. This puts a limit on the stiffness of high-density matter, and therefore on the size of neutron stars, which closely corresponds to the tidal deformability. Our upper limit is consistent with observational information from the observation of gravitational waves emanating from a neutron star-neutron star binary [6, 7].
Another system that produces gravitational waves is one made of two black holes. We study such systems, specically ones where one black hole is much more massive than the other. The gravitational waves sourced by these systems will not be observable by LIGO, but will require a space-based gravitational wave detector. We use a scalar point charge as a toy model for the smaller black hole and apply a method discovered by Hikida et al. [8, 9] to compute the self-force on an accelerated scalar charge in circular orbit analytically through 6th Post-Newtonian order. Our results are compatible with previous Post-Newtonian calculations  and with numerical work on accelerated scalar charges .
Finally, we extend the method of Hikida et al. to the gravitational case. In particular, we calculate a gauge-invariant quantity discovered by Detweiler  through 6th Post-Newtonian order. We also calculate the time derivative of that quantity, which gives the power of the radiated gravitational waves. Interestingly, we find that if the Equivalence Principle is not obeyed and freely-falling particles can follow non-geodesic paths, dipolar gravitational radiation is produced. When we do enforce the Equivalence Principle, our results are consistent with previous Post-Newtonian calculations [12, 13].
Van Oeveren, Eric, "Neutron Star Tidal Deformability and Gravitational Self-force" (2018). Theses and Dissertations. 1938.