The general theory of relativity (GR), a theory of the geometry of physical space-tine, is usually (or at least often) considered as a classical field theory with the basic field being the (pseudo-Riemannian) metric tensor along with its associated connection field and curvature tensor with many similarities (e.g. a Cauchy evolution) to that of most field theories. In this work we will present an alternate point of view or reformulation of GR (with new variables) that appears not to have any analogous reformulation in other field theories. In this reformulation, the fundamental variables are families of surfaces and a scalar function; the standard variables, i.e., the metric tensor, etc., now become derived concepts. These surfaces, which are described by partial differential equation, become the characteristic surfaces of a conformal metric which is obtained directly from the surfaces themselves. The scalar function is a conformal factor turning the conformal metric into an Einstein metric. We emphasize that though, neither the presentation nor the final equations resemble the standard version of GR, the final results are identical to GR.
We briefly mention several technical difficulties working with these equations and then speculate on their usefulness in both "practical" problems and in fundamental issues.