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

preprint

posted on 2006-02-03, 12:30 authored by G.A. Alekseev, Jerry GriffithsFor 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.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

128547 bytes## Publication date

2000## Notes

This is a pre-print. The definitive version: ALEKSEEV, G.A. and GRIFFITHS, J.B., 2000. Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies. Physical Review Letters, 84(23), pp.5247-5250.## Language

- en