General magnetized Weyl solutions: Disks and motion of charged particles

TL;DR

This paper constructs new exact solutions to Einstein-Maxwell equations describing magnetized gravitational fields and thin disks, analyzing charged particle motion and stability in these complex spacetime configurations.

Contribution

It introduces three families of magnetized axisymmetric solutions using Ernst's formalism, including magnetized disk models and their effects on charged particle dynamics.

Findings

Magnetized solutions include magnetized Erez-Rosen and Morgan-Morgan types.

Magnetic fields enable charged particles to move both prograde and retrograde inside disks.

Explicit analysis of particle stability and motion in these magnetized spacetimes.

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.