Exact General Relativistic Disks with Magnetic Fields

TL;DR

This paper extends a method to generate exact models of hot, magnetized disks in general relativity, revealing how magnetic fields and currents influence disk stability and properties, marking the first such models studied in this context.

Contribution

It introduces a novel extension of the 'displace, cut, and reflect' method to Einstein-Maxwell solutions, creating the first models of hot, magnetized disks in general relativity.

Findings

Magnetic fields can alter disk stability in complex ways.

Distributions of currents inside the disk affect magnetic field configurations.

The models demonstrate the impact of magnetic fields on disk properties and stability.

Abstract

The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to construct models of hot disks with surface density, azimuthal pressure, and azimuthal current. The solutions are closely related to Kerr, Taub-NUT, Lynden-Bell-Pinault and to a one-soliton solution. We find that the presence of the magnetic field can change in a nontrivial way the different properties of the disks. In particular, the pure general relativistic instability studied by Bicak, Lynden-Bell and Katz [Phys. Rev. D47, 4334, 1993] can be enhanced or cured by different distributions of currents inside the disk. These currents, outside the disk, generate a variety of axial symmetric magnetic fields. As far as we know these are the first models of hot disks studied in the context of general relativity.