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On the integration of the Einstein equations by the inverse scattering method. (Russian) Zbl 0553.53041
In his investigations on the integrability of the Einstein equations D. Maison has proved integration theorems for gravitational fields, the metric tensor of which allows a representation in the form of functions of only two variables [Phys. Rev. Lett. 41, 521-525 (1978)]. He used the inverse scattering method. Generalizing those results now the integration of the Einstein equations on four-dimensional manifolds is investigated. The associated coefficients depend only on two variables, but the corresponding metric tensor may depend on all four coordinates of the manifold.
Reviewer: K.Barckow
MSC:
53B50 Applications of local differential geometry to the sciences
35P25 Scattering theory for PDEs
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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