Geodesic
Finite-gap solutions of the stationary axisymmetric Einstein equation in vacuum
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 25-41

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_1988_77_1_a2,
     author = {D. A. Korotkin},
     title = {Finite-gap solutions of the stationary axisymmetric {Einstein} equation in vacuum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {25--41},
     publisher = {mathdoc},
     volume = {77},
     number = {1},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a2/}
}
TY  - JOUR
AU  - D. A. Korotkin
TI  - Finite-gap solutions of the stationary axisymmetric Einstein equation in vacuum
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1988
SP  - 25
EP  - 41
VL  - 77
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a2/
LA  - ru
ID  - TMF_1988_77_1_a2
ER  - 
%0 Journal Article
%A D. A. Korotkin
%T Finite-gap solutions of the stationary axisymmetric Einstein equation in vacuum
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1988
%P 25-41
%V 77
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a2/
%G ru
%F TMF_1988_77_1_a2
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/