Geodesic
Solutions of two-dimensional einstein equations parametrized by arbitrary functions and generated by the O(2, 1) $\sigma$ model
Teoretičeskaâ i matematičeskaâ fizika, Tome 64 (1985) no. 1, pp. 51-60 
M. G. Tseitlin. Solutions of two-dimensional einstein equations parametrized by arbitrary functions and generated by the O(2, 1) $\sigma$ model. Teoretičeskaâ i matematičeskaâ fizika, Tome 64 (1985) no. 1, pp. 51-60. http://geodesic.mathdoc.fr/item/TMF_1985_64_1_a5/
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     title = {Solutions of two-dimensional einstein equations parametrized by arbitrary functions and generated by the {O(2,} 1) $\sigma$ model},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Solutions, parametrized by arbitrary functions, of the two-dimensional Einstein equations are constructed by making a special choice of the determinant of the metric and using solutions of the attxiliary $O(2,1)$ $\sigma$ model. These solutions generalize ones considered earlier [1]. The construction is also applied to the Einstein–Maxwell equations and to the case when matter with equation of state $\varepsilon=p$ is present.

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