Chairperson, Graduate Committee: Nicolas YunesSaffer, AlexanderKent Yagi and Nicolas Yunes were co-authors of the article, 'The gravitational wave stress-energy (pseudo)-tensor in modified gravity' in the journal 'Classical and quantum gravity' which is contained within this thesis.Nicolas Yunes was a co-author of the article, 'Angular momentum loss for a binary system in Einstein-aether theory' in the journal 'Physical review D' which is contained within this thesis.Hector O. Silva is an author and Nicolas Yunes is a co-author of the article, 'The exterior spacetime of relativistic stars in scalar-Gauss-Bonnet gravity' submitted to the journal 'Physical review D' which is contained within this thesis.2019-10-212019-10-212019https://scholarworks.montana.edu/handle/1/15591The recent detection of coalescing black holes by the Laser Interferometer Gravitational-wave Observatory has brought forth the era of gravitational wave astronomy. Physicists are only now beginning to probe the mergers of compact objects that send ripples through space and time. These distortions carry with them the information from the system where they originated. The dynamics of black hole collisions and neutron star mergers are new and exciting events which were undetectable just a few years ago. Einstein's theory of General Relativity has done an excellent job of describing gravity and the information that can be extracted from gravitational systems. However, his theory contains several anomalies such as the inability to explain the inflation of the universe, the effects of dark matter and energy, the presence of singularities, as well as a failure to reconcile with quantum mechanics. Modified theories of gravity have been proposed to answer any remaining questions about gravitation while prescribing solutions to the problems General Relativity still has. The work within this thesis describes how we may study modified theories of gravity in the strong field regime through two different means. The first, is through the calculation of the rate of gravitational radiation from binary systems. This rate varies depending on the theory of gravity being studied. Comparing the theoretical predictions of these rates from alternative theories to astronomical observation will allow us to place better constraints on modified gravity and test General Relativity like never before. The second way is through the investigation of the spacetime surrounding a neutron star. Unlike black holes which emit no light, we are able to see neutron stars (more specifically pulsars) through their light curve as they rotate. The shape of the light curve is dictated by the theory of gravitation used to describe the spacetime around the neutron star. My goal of constructing such a spacetime for neutron stars in modified gravity allows for future scientists to study the light curves to be detected and place constraints on the particular theory.enGeneral relativity (Physics)Neutron starsMultiple starsGravitational wavesDissertationCopyright 2019 by Alexander George Saffer