Geodesic
Finite-gap solutions of the stationary axisymmetric Einstein equation in vacuum
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 25-41 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new and large class of exact solutions of the stationary axisymmetric Einstein equation, which are expressed in terms of the Riemann $\theta$ function, is constructed. The properties of the constructed “finite-gap” solutions differ significantly from those of the well-known finite-gap solutions (for example, of the Korteweg–de Vries equation and the nonlinear Schrödinger equation). In particular, the dependence on the dynamical variables in the final expressions is given by a trajectory on a manifold of moduli of algebraic curves, and not on the Jacobi manifold of a given curve. In a degenerate case the constructed solutions include all the main known solutions that can be expressed in terms of elementary functions. 
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     title = {Finite-gap solutions of the stationary axisymmetric {Einstein} equation in vacuum},
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     pages = {25--41},
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     volume = {77},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a2/}
}
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D. A. Korotkin. Finite-gap solutions of the stationary axisymmetric Einstein equation in vacuum. Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 25-41. http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a2/

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