Static charged fluid around a massive magnetic dipole

TL;DR

This paper presents an exact Einstein-Maxwell solution describing a static charged fluid around a magnetic dipole, with thermodynamic analysis indicating its relevance for modeling magnetized charged stellar objects.

Contribution

It provides a new analytical solution coupling a static charged fluid with a magnetic dipole within Einstein-Maxwell theory, extending known solutions like Gutsunaev-Manko and Schwarzschild.

Findings

Solution recovers known limits like Schwarzschild and Gutsunaev-Manko

Thermodynamic quantities suggest relevance for magnetized stellar objects

The model describes a charged fluid around a magnetic dipole

Abstract

An analytical solution of Einstein-Maxwell equations with a static fluid as a source is presented. The spacetime is represented by the axially symmetric Weyl metric and the energy-momentum tensor describes a coupling of a fluid with an electromagnetic field. When appropriate limits are performed we recover the well-known solutions of Gutsunaev-Manko and Schwarzschild. Also, using Eckart's thermodynamics, we calculated the temperature, the mechanical pressure, the charge density and the energy density of the system. The analysis of thermodynamic quantities suggests that the solution can be used to represent a magnetized compact stellar object surrounded by a charged fluid.