An infinite family of magnetized Morgan-Morgan relativistic thin disks

TL;DR

This paper derives a family of exact Einstein-Maxwell solutions describing magnetized, finite, static thin disks using the Horský-Mitskievitch conjecture, with physically reasonable properties despite non-asymptotic flatness.

Contribution

It introduces a new class of magnetized thin disk solutions in general relativity, extending previous models with finite mass and realistic physical behavior.

Findings

Finite disk masses confirmed

Magnetic fields exhibit acceptable physical behavior

Solutions are expressed in oblate spheroidal coordinates

Abstract

Applying the Horsk\'y-Mitskievitch conjecture to the empty space solutions of Morgan and Morgan due to the gravitational field of a finite disk, we have obtained the corresponding solutions of the Einstein-Maxwell equations. The resulting expressions are simply written in terms of oblate spheroidal coordinates and the solutions represent fields due to magnetized static thin disk of finite extension. Now, although the solutions are not asymptotically flat, the masses of the disks are finite and the energy-momentum tensor agrees with the energy conditions. Furthermore, the magnetic field and the circular velocity show an acceptable physical behavior.