Equilibrium solutions of relativistic rotating stars with mixed poloidal and toroidal magnetic fields

TL;DR

This paper numerically constructs stationary, axisymmetric models of relativistic rotating stars with strong mixed magnetic fields, revealing non-circular spacetime structures and providing initial results for highly deformed magnetized stars.

Contribution

It introduces a numerical method to obtain equilibrium solutions of rotating stars with mixed magnetic fields in full Einstein-Maxwell framework, including non-circular spacetime effects.

Findings

First models of highly deformed magnetized rotating stars with mixed fields.

Demonstrates non-circular spacetime due to magnetic field components.

Provides a foundation for future studies of magnetized compact stars.

Abstract

Stationary and axisymmetric solutions of relativistic rotating stars with strong mixed poloidal and toroidal magnetic fields are obtained numerically. Because of the mixed components of the magnetic field, the underlying stationary and axisymmetric spacetimes are no longer circular. These configurations are computed from the full set of the Einstein-Maxwell equations, Maxwell's equations and from first integrals and integrability conditions of the magnetohydrodynamic equilibrium equations. After a brief introduction of the formulation of the problem, we present the first results for highly deformed magnetized rotating compact stars.