A classification is performed of the spaces with plane-wave metrics in accordance with the presence of three-dimensional subgroups of the group of space-time motion with three-dimensional spatial orbits. In order to obtain spatially-homogeneous models, exact solutions to Einstein’s vacuum equations are found. To obtain these solutions, the Petrov and Bianchi classifications are performed. The results obtained on the classification of the plane-wave metrics using the assumed or three-dimensional subgroups of the group of motion with three-dimensional spatial orbits can be used for any metric gravitational theories.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 96–102, February, 2019.
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Osetrin, E.K., Osetrin, K.E. & Filippov, A.E. Plane Gravitational Waves in Spatially-Homogeneous Models of type-(3.1) Stäckel Spaces. Russ Phys J 62, 292–301 (2019). https://doi.org/10.1007/s11182-019-01711-1
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DOI: https://doi.org/10.1007/s11182-019-01711-1