# New code for equilibriums and quasiequilibrium initial data of compact objects. IV. Rotating relativistic stars with mixed poloidal and toroidal magnetic fields

## TL;DR

This paper introduces a new computational code for modeling strongly magnetized, rapidly rotating compact stars with mixed magnetic field components in full general relativity, revealing potential internal magnetic structures.

## Contribution

The paper develops a novel code that solves Einstein-Maxwell-MHD equations for magnetized rotating stars with mixed poloidal and toroidal fields in non-circular spacetimes, advancing modeling capabilities.

## Key findings

- Successfully computed highly magnetized star solutions
- Found matter expulsion from regions of strongest toroidal fields
- Conjecture of internal toroidal vacuum regions in extreme cases

## Abstract

A new code for computing fully general relativistic solutions of strongly magnetized rapidly rotating compact stars is developed as a part of the COCAL (Compact Object CALculator) code. The full set of Einstein's equations, Maxwell's equations and magnetohydrodynamic equations are consistently solved assuming perfect conductivity, stationarity, and axisymmetry, and strongly magnetized solutions associated with mixed poloidal and toroidal components of magnetic fields are successfully obtained in generic (non-circular) spacetimes. We introduce the formulation of the problem and the numerical method in detail, then present examples of extremely magnetized compact star solutions and their convergence tests. It is found that, in extremely magnetized stars, the stellar matter can be expelled from the region of strongest toroidal fields. Hence we conjecture that a toroidal electro-vacuum region may appear inside of the extremely magnetized compact stars, which may seem like the neutron star becoming the strongest toroidal solenoid coil in the universe.