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

TL;DR

This paper develops an infinite hierarchy of exact solutions for Einstein and Einstein-Maxwell equations, describing interacting waves and inhomogeneous cosmologies, using a novel monodromy transform approach.

Contribution

It introduces a new method for generating infinite hierarchies of exact solutions for complex space-times with two spacelike isometries.

Findings

Contains known solutions as special cases

Uses monodromy transform and linear integral equations

Applicable to inhomogeneous cosmological models and wave interactions

Abstract

For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so called `monodromy transform' approach and our new method for the solution of the linear singular integral equation form of the reduced Einstein equations. The solutions presented, which describe inhomogeneous cosmological models or gravitational and electromagnetic waves and their interactions, include a number of important known solutions as particular cases.