Testing theories of gravity by gravitational wave observations.

In this dissertation, Einstein-æther theory is studied. As a candidate of modified theories to general relativity, Einstein-æther theory shows some different features compared to Einstein’s theory. The studies of these features can serve for the test and development of gravitational theories. In this dissertation, the study of Einstein-æther theory is closely related to the gravitational wave observations. In fact, those observations can potentially provide a variety of ways to test general relativity and put severe constraints on Einstein-æther theory. This thesis will mainly focus on the gravitational waves emitted by compact celestial bodies in the universe, and calculate the gravitational waveforms, innermost stable circular orbits, universal horizons, quasi-normal modes, etc. in the framework of Einstein-æther theory. With the continuous improvement of the accuracy of detectors around the world, as well as the accumulation of gravitational wave events, these investigations will become more and more important for understanding the nature of gravity and the dynamics of the universe.