Integrability of geodesics of totally geodesic metrics
Abstract
Analysis of the geodesics in the space of signature (1,3) that splits in two-dimensional distributions resulting from the Weyl tensor eignespaces - hyperbolic and elliptic ones - described in [V. Lychagin, V. Yumaguzhin, Differential invariants and exact solutions of the Einstein equations, Anal.Math.Phys. 1664-235X 1-9 (2016)] are presented. Cases when geodesic equations are integrable are identified. Similar analysis is performed for the same model coupled to Electromagnetism described in [V. Lychagin, V. Yumaguzhi, Differential invariants and exact solutions of the Einstein-Maxwell equation, Anal.Math.Phys. 1, 19--29, (2017)].
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