Prolongation structure and linear eigenvalue equations for Einstein-Maxwell fields

Abstract

The Einstein-Maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials. The prolongation structure in the spirit of Wahlquist and Estabrook (1975)) of the Einstein-Maxwell equations contains the SU(2,1) Lie algebra. A new mapping of known solutions to other solutions has been found.