Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in the Stackel spaces of type (1.1)

Abstract

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that Hamilton-Jacobi equation and Klein-Gordon-Fock equation for a charged test particle can be integrated by the method of complete separation of variables are found. The separation is carried out using the complete sets of mutually-commuting integrals of motion of type (1.1). Whereby in a privileged coordinate system the given equations turn into parabolic type equations. Hence, these metrics can be used as models for describing plane gravitational waves.

arXiv commentThe article will be published in IJGMMP

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• Maxwell equations in homogeneous spaces with solvable groups of motions
• Deviation of geodesics and particle trajectories in a gravitational wave of the Bianchi type VI universe
• New conservation laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar field
• Gravitational Waves of Type III Shapovalov Spacetimes: Particle Trajectories, Geodesic Deviation and Tidal Accelerations
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• Gravitational wave of the Bianchi VII universe: particle trajectories, geodesic deviation and tidal accelerations
• Wave-like exact models with symmetry of spatial homogeneity in the quadratic theory of gravity with a scalar field