Abstract
A classification of conformally flat space-times, admitting complete separation of variables in the eikonal equation, is carried out. The metric tensors, corresponding to different complete sets of integrals of motion, are found. With these metrics, as an example, some solutions to the Einstein equations with a cosmological constant are obtained. For the space-times obtained, examples of integration of the eikonal and scalar field equations are presented.
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Obukhov, V.V., Osetrin, K.E. & Rybalov, Y.A. Conformally flat spaces admitting complete separation of variables in the eikonal equation. Gravit. Cosmol. 14, 104–108 (2008). https://doi.org/10.1134/S0202289308010143
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DOI: https://doi.org/10.1134/S0202289308010143