Geodesic
The isomonodromic deformations and similarity solutions of the Einstein--Maxwell equations
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 11, Tome 181 (1990), pp. 65-92

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It is shown that self-similar solutions of the Einstein-Maxwell equations in the axially symmetric case describe isomonodromic deformations of ordinary differential equations with rational coefficients. New types of these solutions that expressed in terms of fifth Painleve trancedent are found. 
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     author = {A. V. Kitaev},
     title = {The isomonodromic deformations and similarity solutions of the {Einstein--Maxwell} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {65--92},
     publisher = {mathdoc},
     volume = {181},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_181_a2/}
}
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A. V. Kitaev. The isomonodromic deformations and similarity solutions of the Einstein--Maxwell equations. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 11, Tome 181 (1990), pp. 65-92. http://geodesic.mathdoc.fr/item/ZNSL_1990_181_a2/