# Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein’s field equations

@article{Alekseev2005MonodromydataPO, title={Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein’s field equations}, author={George A. Alekseev}, journal={Theoretical and Mathematical Physics}, year={2005}, volume={143}, pages={720-740} }

We show that for the fields depending on only two of the four space-time coordinates, the spaces of local solutions of various integrable reductions of Einstein’s field equations are the subspaces of the spaces of local solutions of the “null-curvature” equations selected by universal (i.e., solution-independent conditions imposed on the canonical (Jordan) forms of the desired matrix variables. Each of these spaces of solutions can be parameterized by a finite set of holomorphic functions of…

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