Frameworks for analyzing and testing theories of gravity

Theoretical frameworks are presented for the analysis and testing of gravitation theories--both metric and nonmetric. For nonmetric theories, the high precision Eotvos--Dicke--Braginskii (EBD) experiments are demonstrated to be powerful tests of their gravitational coupling to electromagnetic interactions. All known nonmetric theories are ruled out to within the precision of the EDB experiments. A new metric theory of gravity is presented that cannot be distinguished from general relativity in all current and planned solar system experiments. However, this theory has very different gravitational-wave properties. Hence, the need for further tests of metric theories beyond the Parametrized Post--Newtonian formalism is pointed out and the importance of the observation of gravitational waves as a tool for testing relativistic gravity in the future is emphasized. A theory-independent formalism delineating the properties of weak, plane gravitational waves in metric theories is set up. General conservation laws that follow from variational principles in metric theories of gravity are investigated. (U.S.)