Conformal two-structure as the gravitational degrees of freedom in general relativity

Abstract

In this paper, we suggest that what we shall call the conformal 2-structure may, in an appropriate coordinate system, serve to embody the two gravitational degrees of freedom of the Einstein (vacuum) field equations. The conformal 2-structure essentially gives information concerning the manner in which a family of 2-surfaces is embedded in a 3-surface. We show that, formally at least, this prescription works for the exact plane and cylindrical gravitational wave solutions, for the double-null and null-timelike characteristic initial value problems, and for the usual Cauchy spacelike initial value problem. We conclude with a preliminary consideration of a two-plus-two breakup of the field equations aimed at unifying these and other initial value problems; and a discussion of some aspirations and remaining problems of this approach.