A new formulation of the field equations for the stationary axisymmetric vacuum gravitational field. I. General theory

Publisher Website
Google Scholar
Abstract
A new formulation of the stationary axisymmetric vacuum gravitational field equations which is substantially different from the well known formulations of Lewis and Ernst is presented. The basic variable is e2γ = -g11g44 and satisfies a field equation of the fourth differential order which may be interpreted as the condition that a certain 2-space has constant curvature, K = -1. The principal motivation is that for many known solutions and all known asymptotically flat (non-static) solutions, e2γ takes a much simpler functional form than either the metric coefficients, g44, g34 and g33, or the Ernst potentials, E and ξ . Three methods are given for the construction of the full metric from e2γ. A duality principle is invoked to provide a very similar field equation for the metric coefficient, e2γ-2u = -g11.