Relativistic static magnetized finite thin disk: An infinite family of exact solutions

TL;DR

This paper presents an infinite family of exact solutions for relativistic finite thin disks with magnetic fields, solving Einstein-Maxwell equations and ensuring physical plausibility with finite mass and energy conditions.

Contribution

It introduces a new class of exact solutions for magnetized thin disks in relativity using the Horský-Mitskievitch method, extending known models.

Findings

Finite mass and energy conditions satisfied.

Explicit expressions for magnetic field and circular velocity.

Solutions reduce to Morgan and Morgan vacuum case.

Abstract

An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horsk\'y-Mitskievitch generating conjecture. The vacuum limit of these obtained solutions is the well known Morgan and Morgan solution. The obtained expressions are simply written in terms of oblate spheroidal coordinates. The mass of the disks are finite and the energy-momentum tensor agrees with all the energy conditions. The magnetic field and the circular velocity are evaluated explicitly. All the physical quantities obtained shown an acceptable