General magnetized Weyl solutions: disks and motion of charged particles |
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Authors: | Cristian H García-Duque Gonzalo García-Reyes |
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Institution: | 1.Departamento de Física,Universidad Tecnológica de Pereira,Pereira,Colombia |
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Abstract: | We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical
coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized spheroidal coordinates
which is a generalization of the previous systems. The method used to build such solutions is the well-known complex potential
formalism proposed by Ernst, using as seed solutions vacuum solutions of the Einstein field equations. We show explicitly
some particular solutions among them a magnetized Erez-Rosen solution and a magnetized Morgan-Morgan solution, which we interpret
as the exterior gravitational field of a finite dislike source immersed in a magnetic field. From them we also construct using
the well known “displace, cut and reflect” method exact solutions representing relativistic thin disks of infinite extension.
We then analyze the motion of electrically charged test particles around these fields for equatorial circular orbits and we
discuss their stability against radial perturbations. For magnetized Morgan-Morgan fields we find that inside of disk the
presence of magnetic field provides the possibility of to find relativist charged particles moving in both prograde and retrograde
direction. |
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