GR VIA CHARACTERISTIC SURFACES

We reformulate the Einstein equations as equations for families of surfaces on a four-manifold. These surfaces eventually become characteristic surfaces for an Einstein metric (with or without sources). In particular they are formulated in terms of two functions on R(4)xS(2), i.e., the sphere bundle over space-time, one of the functions playing the role of a conformal factor for a family of associated conformal metrics, the other function describing an S-2's worth of surfaces at each spacetime point. It is from these families of surfaces themselves that the conformal metric, conformal to an Einstein metric, is constructed; the conformal factor turns them into Einstein metrics. The surfaces are null surfaces with respect to this metric. (C) 1995 American Institute of Physics.