Gravitational solitons and monodromy transform approach to solution of integrable reductions of Einstein equations

In this paper the well known Belinskii and Zakharov soliton generating tran sformations of the solution space of vacuum Einstein equations with two-dim ensional Abelian groups of isometries are considered in the context of the so-called "monodromy transform approach", which provides some general base for the study of various integrable space-time symmetry reductions of Einst ein equations. Similarly to the scattering data used in the known spectral transform, in this approach the monodromy data for solution of associated l inear system characterize completely any solution of the reduced Einstein e quations, and many physical and geometrical properties of the solutions can be expressed directly in terms of the analytical structure on the spectral plane of the corresponding monodromy data functions. The Belinskii and Zak harov vacuum soliton generating transformations can be expressed in explici t form (without specification of the background solution) as simple (linear -fractional) transformations of the corresponding monodromy data functions with coefficients, polynomial in spectral parameter. This allows to determi ne many physical parameters of the generating soliton solutions without (or before) calculation of all components of the solutions. The similar charac terization for electrovacuum soliton generating transformations is also pre sented. (C) 2001 Published by Elsevier Science B.V.