Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies
preprintposted on 03.02.2006, 12:30 by G.A. Alekseev, Jerry Griffiths
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein equations for vacuum and the Einstein–Maxwell equations for electrovacuum fields as represented by their Ernst potentials.These solutions are parametrized by three arbitrary rational functions of an auxiliary complex parameter and, therefore, depend on an arbitrarily large number of free parameters.They are constructed using a linear singular integral equation.This arises in the context of the so called “monodromy transform” approach, and is equivalent to the usual partial derivative form of space-time symmetry reduced Einstein equations.The solutions presented can be used to describe various inhomogeneous cosmological models, or gravitational and electromagnetic waves and their interactions. They include a number of important known solutions as particular cases.
- Mathematical Sciences