Gravitational-wave observations as a tool for testing relativistic gravity

Gravitational-wave observations can be powerful tools in the testing of relativistic theories of gravity - perhaps the only tools for distinguishing between certain extant theories in the foreseeable future. In this paper we examine gravitational radiation in the far field using a formalism that encompasses all 'metric theories of gravity.' There are six possible modes of polarization, which can be completely resolved by feasible experiments. We set forth a theoretical framework for classification of waves and theories, based on the Lorentz transformation properties of the six modes. We also show in detail how the six modes may be experimentally identified and to what extent such information limits the 'correct' theory of gravity.