Geodesic
Self-similar solutions of the equations of general relativity associated with the solutions of P-type equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 155-160

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A study is made of the connection between self-similar solutions of the Ernst and Einstein–Maxwell equations and the solutions of equations without moving critical points. Two forms of partial differential equations are found that have the Ernst equation as a special ease. The solutions of these equations can be expressed in terms of the solutions of the fifth Painlevé equation. 
@article{TMF_1984_61_1_a14,
     author = {V. V. Tsegel'nik},
     title = {Self-similar solutions of the equations of general relativity associated with the solutions of {P-type} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {155--160},
     publisher = {mathdoc},
     volume = {61},
     number = {1},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a14/}
}
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V. V. Tsegel'nik. Self-similar solutions of the equations of general relativity associated with the solutions of P-type equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 155-160. http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a14/