INTRODUCTION

In China, I have learned, there is a valuable tradition: to appreciate and show great respect for one's teachers. Undoubtedly, the most successful method of teaching is by example. Certainly this was true in my case. Charles W. Misner was a pioneer in applying modern differential geometry (Misner 1964) especially differential forms (Misner and Wheeler 1957) to gravitational theory, in investigating the canonical Hamiltonian formulation of gravity, and in formulating suitable expressions for conserved quantities, in particular mass-energy (Arnowitt, Deser and Misner (ADM) 1962). I have, as this work indicates, at least to some extent, followed my teacher's directions.

The outline of this work is as follows. First, differential form methods are used to obtain a covariant Hamiltonian formulation for any gravitational theory. The Hamiltonian includes a covariant expression for the conserved quantities of an asymptotically flat or constant curvature space. Next the positive total energy test, a promising and appropriate theoretical test for alternate gravitational theories, is described. The final topic concerns application to Einstein gravity of new rotational gauge conditions and their associated special orthonormal frames. These frames provide a good localization of energy and parameterization of solutions.

COVARIANT HAMILTONIAN FORMALISM

There are significant benefits in the canonical Hamiltonian formulation of a theory, in particular the identification of constraints, gauges, degrees of freedom and conserved quantities (Isenberg and Nester 1980), however the usual approach (e.g., in Misner, Thorne and Wheeler (MTW) 1973 and ADM 1962) exacts a heavy price: the loss of manifest 4-covariance. Differential form techniques can be used to largely avoid this cost (Nester 1984).