MG11 
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Monodromy Transform Approach in the Theory of Integrable Reductions of Einstein's Field Equations and some applications

Monodromy transform approach provides a unified general method for solving of various two-dimensional integrable space-time symmetry reductions of Einstein's field equations in General Relativity and in some string gravity models. Technically, it allows to reduce the problem to solution of some basic system of linear singular integral equations on the spectral plane. Among different applications of this approach to constructing of stationary axisymmetric fields, solving characteristic initial value problems for colliding waves and inhomogeneous cosmologies, we concentrate in this talk on the constructing of new solutions for black holes interacting with external gravitational and electromagnetic fields and describe some related features of the black hole dynamics.