Linearized Einstein theory via null surfaces

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Abstract
Recently there has been developed a reformulation of general relativity (GR)—referred to as the null surface version of GR—where instead of the metric field as the basic variable of the theory, families of three‐surfaces in a four‐manifold become basic. From these surfaces themselves, a conformal metric, conformal to an Einstein metric, can be constructed. A choice of conformal factor turns it into an Einstein metric. The surfaces are then automatically characteristic surfaces of this metric. In the present paper we explore the linearization of this null surface theory and compare it with the standard linear GR. This allows a better understanding of many of the subtle mathematical issues and sheds light on some of the obscure points of the null surface theory. It furthermore permits a very simple solution generating scheme for the linear theory and the beginning of a perturbation scheme for the full theory.
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