Coordinate modelling for static axially symmetric electrovac metrics

A new technique of coordinate modelling is introduced. It is shown that the static axially symmetric electrovac field equations are easier to solve in terms of coordinates which are specially adapted to the electrostatic equipotential contours of the system. Several new exact solutions are readily found by separating variables and by employing complex analytic functions. A framework for the construction of general solutions of the axially symmetric electrostatic vacuum field equations is presented and the Weyl solutions are shown to be trivially extractable.