From Schwarzschild to Kerr: Generating spinning Einstein-Maxwell fields from static fields

The Kerr solution is generated from the Schwarzschild solution by a simple combination of real global coordinate transformations and of invariance transformations acting on the space of stationary solutions of the Einstein-Maxwell equations. The same transformation can be used to generate a spinning field configuration from any static axisymmetric configuration. We illustrate this by generating from the continuous family of Voorhees-Zipoy vacuum solutions a family of solutions endowed with mass, angular momentum, dipole magnetic moment, and quadrupole electric moment.