Abstract
•New exact solutions of Einstein-Maxwell field equations in pure magnetic fields, in correspond to the Bonnor metric are obtained.•Solutions are obtained in spherical coordinates with the use of Lie symmetry method.•Obtained solutions are accelerating static solutions of Einstein-Maxwell equations for a non-conformally flat semi-Riemannian manifold.•The graphical representations in 3D are also shown.
The Bonnor field shed light on imposition of two magnetic poles, both with mass m, and strengths -m and m, that are situated at a coordinate distance 2b on a symmetry axis. With the addition of an external magnetic field, these magnetic monopoles can be kept apart in an equilibrium. The new exact solutions of Einstein-Maxwell field equations in pure magnetic fields, in correspond to the Bonnor metric, are obtained in spherical coordinates with the use of Lie symmetry method. The obtained solutions are accelerating static solutions of Einstein-Maxwell equations in a more general form, for a semi-Riemannian manifold which is not conformally flat. The graphical representations in 3D are also shown.