Geodesic
Equilibrium distributions of the charged fluids in the space-times with a simple-transitive groups of homothetic motions
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 37-53 
R. A. Daishev; V. A. Karin. Equilibrium distributions of the charged fluids in the space-times with a simple-transitive groups of homothetic motions. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 37-53. http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a4/
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     title = {Equilibrium distributions of the charged fluids in the space-times with a~simple-transitive groups of homothetic motions},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     volume = {148},
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     url = {http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a4/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The method of finding of the exact solutions of the self-consistent Einstein–Maxwell equations system are suggested. It is supposed that the space-time admits simple-transitive group of homothetic transformations and the source of such space-times is the perfect fluid. The proposed method is the generalization of Ozsvath's method of finding of the homogeneous solutions of Einstein field equations. It is supposed also that the fluid's velocity vector is collinear to time-like vector $\mathbf Y$ of the Lie algebra of the group $H_r.$ Under above assumption all exact solutions of the system are found.

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