DYNAMICS OF LIGHT-CONE CUTS OF NULL INFINITY

In this work we explore further consequences of a recently developed a lternate formulation of general relativity, where the metric variable is replaced by families of surfaces as the primary geometric object of the theory-the (conformal) metric is derived from the surfaces-and a conformal factor that converts the conformal metric into an Einstein m etric. The surfaces turn out to be characteristic surfaces of this met ric. The earlier versions of the equations for these surfaces and conf ormal factor were local and included all vacuum metrics (with or witho ut a cosmological constant). In this work, after first reviewing the b asic theory, we specialize our study to spacetimes that are asymptotic ally flat. In this case our equations become considerably simpler to w ork with and the meaning of the variables becomes much more transparen t. Several related insights into asymptotically flat spaces have resul ted from this. (1) We have shown (both perturbatively and nonperturbat ively for spacetimes close to Minkowski space) how a ''natural'' choic e of canonical coordinates can be made that becomes the standard Carte sian coordinates of Minkowski space in the flat limit. (2) Using these canonical coordinates we show how a simple (completely gauge-fixed) p erturbation theory off flat space can be formulated. (3) Using the rig id structure of the spacetime null cones (with their intersection with future null infinity) we show how the asymptotic symmetries (the EMS group or rather its Poincare subgroup) can be extended to act on the i nterior of the spacetimes. This apparently allows us to define approxi mate Killing vectors and approximate symmetries. We also appear to be able to define a local energy-momentum vector field that is closely re lated to the asymptotic Bondi energy-momentum four-vector. [S0556-2821 (97)04420-2]. PACS number(s): 04.20.Gz, 04.20.Ha.