New Formulation of the Axially Symmetric Gravitational Field Problem

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Abstract
The field equations governing the gravitational field of a uniformly rotating axially symmetric source are reformulated in terms of a simple variational principle. The new formalism affords a concise unified derivation of the solutions discovered by Weyl and Papapetrou, and permits a simple derivation of the Kerr metric in terms of prolate spheroidal coordinates. More complex solutions are identified by applying perturbation theory.