The Interior Field of a Magnetized Einstein-Maxwell Object

TL;DR

This paper develops a method to solve the interior structure of a magnetized Einstein-Maxwell object by reducing complex equations to simpler Poisson-like equations, allowing for integration and potential matching with exterior solutions.

Contribution

It introduces a harmonic map ansatz approach to simplify Einstein-Maxwell equations for magnetized fluids, enabling explicit interior solutions and matching with exterior fields.

Findings

Successfully reduced Einstein-Maxwell equations to Poisson-like equations.

Derived interior solutions for magnetized Einstein-Maxwell objects.

Identified conditions for matching interior and exterior solutions.

Abstract

Using the Harmonic map ansatz, we reduce the axisymmetric, static Einstein-Maxwell equations coupled with a magnetized perfect fluid to a set of Poisson-like equations. We were able to integrate the Poisson equations in terms of an arbitrary function $M=M(\rho,\zeta)$ and some integration constants. The thermodynamic equation restricts the solutions to only some state equations, but in some cases when the solution exists, the interior solution can be matched with the corresponding exterior one.