Null surfaces formulation in three dimensions

The null surface formulation of general relativity is developed for 2+1 dim ensional gravity. The geometrical meaning of the metricity condition is ana lyzed and two approaches to the derivation of the field equations are prese nted. One method makes explicit use of the conformal factor while the other only uses conformal information. The resulting set of equations contains t he same geometrical meaning as the four-dimensional formulation without the technical complexities of the higher dimensional analog. A canonical famil y of null surfaces in this formulation, the light cone cuts of null infinit y, are constructed on asymptotically flat space-times and some of their kin ematical aspects are discussed. A particular example, which nevertheless co ntains most of the generic features, is explicitly constructed and analyzed , revealing the behavior predicted in the full theory. (C) 2000 American In stitute of Physics. [S0022-2488(00)01607-8].