Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies

摘要

For space-times with two spacelike isometries, we present infinitehierarchies of exact solutions of the Einstein and Einstein--Maxwell equationsas represented by their Ernst potentials. This hierarchy contains threearbitrary rational functions of an auxiliary complex parameter. They areconstructed using the so called `monodromy transform' approach and our newmethod for the solution of the linear singular integral equation form of thereduced Einstein equations. The solutions presented, which describeinhomogeneous cosmological models or gravitational and electromagnetic wavesand their interactions, include a number of important known solutions asparticular cases.