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

TL;DR

This paper classifies Stackel space metrics and electromagnetic potentials allowing complete separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for charged particles, facilitating their solution and modeling plane gravitational waves.

Contribution

It identifies all equivalence classes of metrics and potentials enabling variable separation in these equations within Stackel spaces of type (1.1).

Findings

Complete classification of Stackel space metrics for variable separation.

Separation transforms equations into parabolic type in specific coordinates.

Models derived can describe plane gravitational waves.

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.