On a generalization of a soliton solution in general relativity

The Einstein equations in vacuum for a stationary axisymmetric field in the Lewis-Papapetrou form are discussed. Using a method of variation of parameters the authors obtain a class of solutions. The solutions are described as nonlinear superpositions of gravitational soliton solutions in an arbitrary axisymmetric gravitational field. As an application, the authors deduce explicit solutions which reduce to the Kerr metric after an Ehlers transformation.