# Stability aspects of relativistic thin magnetized disks

## TL;DR

This paper constructs exact solutions for thin, magnetized disks in General Relativity using a modified method, analyzing their stability and potential astrophysical relevance.

## Contribution

It introduces a new application of the 'displace, cut and reflect' method to generate stable, magnetized thin disk solutions from known magnetic dipole metrics.

## Key findings

- Many solutions are stable under certain conditions.
- Surface density profiles can resemble ring-like structures.
- Solutions are physically relevant for astrophysical disk scenarios.

## Abstract

We adapt the well known "displace, cut and reflect" method to construct exact solutions of the Einstein-Maxwell equations corresponding to infinitesimally thin disks of matter endowed with dipole magnetic fields, which are entirely supported by surface polar currents on the disk. Our starting point is the Gutsunaev-Manko axisymmetric solution describing massive magnetic dipoles in General Relativity, from which we obtain a continuous three-parameter family of asymptotically flat static magnetized disks with finite mass and energy. For strong magnetic fields, the disk surface density profile resembles some well known self-gravitating ring-like structures. We show that many of these solutions can be indeed stable and, hence, they could be in principle useful for the study of the abundant astrophysical situations involving disks of matter and magnetic fields.