Abstract
This paper presents a new type of spacelike magnetic curves associated with the Sabban vector field defined in the Minkowski space. In this approach, some geometrical and physical features of the moving charged particle corresponding to the spacelike magnetic curves are identified. An entire characterization is developed for spacelike spherical magnetic curves, denoting particularly the changes of their energy with respect to time, the influence of the magnetic force on them, and the existence condition for the uniformity of these curves.
Highlights
De-Sitter spacetime has the Lorentzian space structure such that it has a positive sectional curvature
Focusing on De-Sitter spacetime has numerous advantages when studying astrophysics and relativity theory since it is maximally symmetric but it provides the use of Poincare group construction, which is reduced by the isometry group of the De-Sitter spacetime
A magnetic field on a k-dimensional semi-Riemannian manifold (R, g), which has the Levi–Civita connection ∇, is any closed two-form F on R such that its Lorentz force is a one-to-one anti-symmetric tensor field φ given by g (φ (A), B) = F (A, B), where A, B are any vector fields tangent to R
Summary
De-Sitter spacetime has the Lorentzian space structure such that it has a positive sectional curvature. A magnetic field on a k-dimensional semi-Riemannian manifold (R, g), which has the Levi–Civita connection ∇, is any closed two-form F on R such that its Lorentz force is a one-to-one anti-symmetric tensor field φ given by g (φ (A) , B) = F (A, B) , where A, B are any vector fields tangent to R. A magnetic field on an k-dimensional semi-Riemannian manifold (R, g) is any closed two-form F. A significant feature of magnetic curves is that they have a constant kinetic energy since their speed is a constant This is an obvious result of the anti-symmetricity of the Lorentz force. This paper presents new type of spacelike magnetic curves associated with the Sabban vector field defined in the Minkowski space. The necessary and sufficient conditions of the uniformity of spacelike magnetic curves are identified
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