Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)

Abstract

Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton-Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in a privileged coordinate system the Hamilton-Jacobi equation turns into a parabolic type equation.

References in corpus (12)

• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
• Aspects of Axion $F(R)$ Gravity
• $F(R)$ Gravity with an Axion-like Particle: Dynamics, Gravity Waves, Late and Early-time Phenomenology
• Pure radiation in space-time models that admit integration of the eikonal equation by the separation of variables method
• Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.0)
• Shapovalov wave-like spacetimes
• Exact solutions for scalar field cosmology in f(R) gravity
• The space-time models with dust matter that admit separation of variables in Hamilton-Jacobi equations of a test particle
• Einstein-Maxwell-axion theory: Dyon solution with regular electric field
• The extended Einstein-Maxwell-aether-axion model: Exact solutions for axionically controlled pp-wave aether modes

Cited by in corpus (11)

• Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.0)
• Maxwell's equations in homogeneous spaces for admissible electromagnetic fields
• Algebra of the symmetry operators of the Klein-Gordon-Fock equation for the case when groups of motions $G_3$ act transitively on null subsurfaces of spacetime
• Algebras of integrals of motion for the Hamilton-Jacobi and Klein-Gordon-Fock equations in spacetime with a four-parameter groups of motions in the presence of an external electromagnetic field
• Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in the Stackel spaces of type (1.1)
• Maxwell equations in homogeneous spaces with solvable groups of motions
• Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions
• Exact model of gravitational wave and pure radiation
• Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions
• Exact models of pure radiation in R^2 gravity for spatially homogeneous Shapovalov spacetimes type II
• Wave-like exact models with symmetry of spatial homogeneity in the quadratic theory of gravity with a scalar field