Geodesic
Isomonodromy Approach to Boundary Value Problems for the Ernst Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 85-100

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We use the isomonodromy properties of theta-functional solutions of the Ernst equation and an asymptotic expansion in the spectral parameter to establish algebraic relations, enforced by the underlying Riemann surface, between the metric functions and their derivatives. These relations determine which classes of boundary value problems can be solved on a given surface. The situation on lower-genus Riemann surfaces is studied in detail.
Keywords: general relativity theory
Mots-clés : exact solutions, isomonodromy deformations. 
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     url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a7/}
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C. Klein. Isomonodromy Approach to Boundary Value Problems for the Ernst Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 1, pp. 85-100. http://geodesic.mathdoc.fr/item/TMF_2003_134_1_a7/