Newtonian gravity on the null cone

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Abstract
For a general relativistic ideal fluid, we analyze the Newtonian limit of the initial value problem set on a family of null cones. The underlying Newtonian structure is described using Cartan’s elegant space–time version of Newtonian theory and a limiting process rigorously based upon the velocity of light approaching infinity. We find that the existence of a Newtonian limit imposes a strikingly simple relationship between the gravitational null data (i.e., the shear of the null cones) and the Newtonian gravitational potential. This result has immediate application to numerical evolution programs for calculating gravitational radiation and might serve as the basis for a post‐Newtonian approximation scheme.