Perihelion advance and stability criterion of a spinning charged test particle in Reissner–Nordström field: Application in earth orbit

In this study, a new equation of motion of a spinning charged test particle is examined. This equation is a counterpart of Papapetrou equations in Riemannian geometry when the charge of the particle disappears. By using the Lagrangian approach, the equation of motion of the spinning charged particle is derived. Furthermore, the path deviation of the spinning charged particle is achieved by the same Lagrangian function. The equation of motion of the spinning charged test particle, in the Reissner–Nordström background is entirely solved. The stability criteria of the spinning motion of the charge test particle are discussed. The Perihelion advance and trajectory of a spinning charged test particle, in the Reissner–Nordström space–time, is scrutinized along with two different methods; the first is the perturbation method (Einstein’s method) and the second is described by Kerner et al.[Formula: see text] Moreover, the effect of charge and spin on Perihelion advance are inspected. Additionally, the existing results are matched with the previously cited works. Finally, applications to the Earth’s orbit are also analyzed.

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

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.

Algebras of symmetry operators of Klein-Gordon-Fock equation for groups acting transitively on two-dimensional subspaces of space-time manifold

All external electromagnetic fields are found in which the Klein-Gordon-Fock equation for a charged test particle admits first-order symmetry operators provided that the groups G 3, r £ 3, of motions act transitively on the two-dimensional subspace V 2.

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

We can find 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.

Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)

All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as complete sets of killing vector and tensor fields, are constructed. The results can be used when studying solutions of field equations in the theory of gravity.

The Lagrangian of charged test particle in Horava-Lifshitz black hole and deformed phase space

We use deformation approach and obtain Lagrangian of charged test particle. We show the effect of non-commutative parameters [Formula: see text] and [Formula: see text] on the Lagrangian of a test particle in Horava-Lifshitz background with charge and without charge and see in the case of [Formula: see text] and without charge, the deformed and non-deformed Lagrangian will be the same. In the case of [Formula: see text] and with charge will be the same but the charge or field need some scaling. Finally, results in the case of [Formula: see text] with charge are completely different. It means that we have other components in addition to having a time component of the field.