Maxwell's equations in homogeneous spaces for admissible electromagnetic fields

Abstract

Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion ) that is isomorphic to the algebra of group operators. Two frames associated with the group of motions are used to obtain systems of ordinary differential equations to which Maxwell's equations reduce. The solutions are obtained in quadratures. The potentials of the admissible electromagnetic fields and the metrics of the spaces contained in the obtained solutions depend on six arbitrary time functions, so it is possible to use them to integrate field equations in the theory of gravity.

15 p.p

References in corpus (8)

• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
• 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
• 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)
• Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature
• Vacuum quantum effects on Lie groups with bi-invariant metrics

Cited by in corpus (1)

• Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions