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On the construction of recursion operators for the Kerr-Newman and FRLW metrics. (English) Zbl 1319.83008

The Kerr-Newman metric represents a black hole, and the FRLW metrics represent the Friedmann-Robertson-Lemaitre-Walker universe models. For both types of metrics, the author presents recursion operators which are related to geodesic flows. The result can be applied to find conservation laws within these systems.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
70H20 Hamilton-Jacobi equations in mechanics
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
53D25 Geodesic flows in symplectic geometry and contact geometry
35Q76 Einstein equations
83C10 Equations of motion in general relativity and gravitational theory
83C57 Black holes
83F05 Relativistic cosmology
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