Maxwell equations in homogeneous spaces with solvable groups of motions

Abstract

The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G(VII) is completed. All non-equivalent exact solutions of Maxwell vacuum equations for electromagnetic fields and spaces with such symmetry have been obtained. The vectors of the canonical frame of a homogeneous space of type VII according to the Bianchi classification, and the electromagnetic field potentials have been found.

10 pages. arXiv admin note: text overlap with arXiv:2204.07031

References in corpus (10)

• 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
• Maxwell's equations in homogeneous spaces for admissible electromagnetic fields
• 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
• Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups
• Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in the Stackel spaces of type (1.1)
• New conservation laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar field
• Wave-like spatially homogeneous models of Stackel spacetimes (2.1) type in the scalar-tensor theory of gravity
• The Størmer problem for an aligned rotator
• Symmetry operators and separation of variables in the $(2+1)$-dimensional Dirac equation with external electromagnetic field
• Vacuum quantum effects on Lie groups with bi-invariant metrics

Cited by in corpus (6)

• Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions
• Classification of the non-null electrovacuum solution of Einstein-Maxwell equations with three-parameter abelian group 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
• Secondary gravitational waves against a strong gravitational wave in the Bianchi VI universe
• Induced electromagnetic radiation from a charged cloud in a plane gravitational wave