GR via characteristic surfaces

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Abstract
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×S 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 space–time 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.
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