An almost conformal approach to axial symmetry

A new approach to stationary and axially symmetric gravitational fields in general relativity is outlined. It is based on the conformal properties of the 3-space of Killing trajectories. No smooth limit into Weyl's static metrics is allowed here. Two degenerate classes of fields are excluded, and the Ernst potential with its complex conjugate are introduced as new coordinates. The cylindrical radius is eliminated from the field equations. Two special cases, characterized by conformal flatness, and by Simon flatness, are solved explicitly, and a conformal potential for the general problem is shown to exist. (author)