General magnetized Weyl solutions: Disks and motion of charged particles

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.

25 pages, 9 figuras. Accepted for publication in Gen. Rel. Grav

References in corpus (8)

• Magnetic processes in a collapsing dense core. I Accretion and Ejection
• A magnetically collimated jet from an evolved star
• Off-equatorial orbits in strong gravitational fields near compact objects -- II: halo motion around magnetic compact stars and magnetized black holes
• Magnetorotational collapse of very massive stars to black holes in full general relativity
• Electrovacuum Static Counterrotating Relativistic Dust Disks
• Charged perfect fluid disks as sources of Taub-NUT-type spacetimes
• Counterrotating perfect fluid discs as sources of electrovacuum static spacetimes
• Static charged fluid around a massive magnetic dipole

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• Exact relativistic models of thin disks around static black holes in a magnetic field
• Exact relativistic models of perfect fluid disks in a magnetic field
• Analytical models of finite thin disks in a magnetic field
• Exact relativistic models of conformastatic charged dust thick disks