Construction of exact solutions of the Einstein-Maxwell equations corresponding to a given behaviour of the Ernst potentials on the symmetry axis

The method developed by one of the authors for the construction of exact solutions of the Einstein-Maxwell equations by setting the behaviour of the Ernst potentials on the symmetry axis is discussed in full detail. Some new results regarding the solution of the integral equations and the construction of the 3*3 matrix potential H are presented. Two new examples of the application of the method are considered, one of which is the stationary vacuum solution for a rotating mass, and the second one is the four-parameter metric which can be used for the description of the exterior field of a charged magnetized spinning source.