Gravitational Field Equations for Sources with Axial Symmetry and Angular Momentum

The investigation of stationary axially symmetric gravity fields leads to a reduced system involving two field variables which describe the "Newtonian" and the "rotation" part of the metric. This paper presents a parametrization of this reduced problem which exhibits a previously unnoticed symmetry. Although the symmetry group [isomorphic to homogeneous Lorentz transformations on (2+1)-dimensional space] has a trivial action corresponding to unimodular linear transformations of the $\phi t$ coordinate pair, its existence "explains" the existence of a very simple new Lagrangian for the reduced field equations, and the relatively simple form in which these equations (and the corresponding surface-independent flux integrals for mass and angular momentum) can now be written.