Conservation laws and preferred frames in relativistic gravity. I. Preferred-frame theories and an extended PPN formalism

We present and discuss a revised version of the Parametrized Post-Newtonian (PPN) Formalism. By regrouping the old PPN parameters, we obtain a new set of parameters which are used to classify theories of gravity according to four attributes; curvature of space-geometry, nonlinearity of gravity, existence of a preferred Universal rest-frame, and validity of conservation laws for momentum. We study a variety of preferred-frame theoiies of gravity, and show that new terms must be added to the PPN metric in order to analyze such prdened-frame theories from any chosen frame of reference. These new terms depend on the velocity of the observer's chosen frame relative to the preferred Universal rest-frame singled out by such theories.