General Relativistic Razor-Thin Disks with Magnetically Polarized Matter

TL;DR

This paper introduces new analytical models of magnetized, razor-thin disks in general relativity, providing explicit solutions for their physical properties and demonstrating their potential for astrophysical applications and numerical simulations.

Contribution

It presents a novel family of exact, axially symmetric solutions for magnetized thin disks in Einstein-Maxwell theory, including detailed expressions for physical quantities and conditions for physical plausibility.

Findings

Analytical expressions for surface energy density and pressure.

Solutions satisfy energy conditions and have finite mass.

Models are suitable for astrophysical and numerical applications.

Abstract

The origin of magnetic fields in the universe still remains unknown and constitutes one of the most intriguing questions in astronomy and astrophysics. Their significance is enormous since they have a strong influence on many astrophysical phenomena. In regards of this motivation, theoretical models of galactic disks with sources of magnetic field may contribute to understand the physics behind them. Inspired by this, we present a new family of analytical models for thin disks composed by magnetized material. The solutions are axially symmetric, conformastatic and are obtained by solving the Einstein-Maxwell Field Equations for continuum media without the test field approximation, and assuming that the sources are razor-thin disk of magnetically polarized matter. We find analytical expressions for the surface energy density, the pressure, the polarization vector, the electromagnetic fields, the mass and the rotational velocity for circular orbits, for two particular solutions. In each case, the energy-momentum tensor agrees with the energy conditions and also the convergence of the mass for all the solutions is proved. Since the solutions are well-behaved, they may be used to model astrophysical thin disks, and also may contribute as initial data in numerical simulations. In addition, the process to obtain the solutions is described in detail, which may be used as a guide to find solutions with magnetized material in General Relativity.