Maxwell equation violation by density dependent magnetic fields in neutron stars

TL;DR

This paper demonstrates that common density-dependent magnetic field models in neutron stars violate Maxwell's equations, analyzing the extent of violation across different equations of state and proposing potential solutions.

Contribution

It reveals a fundamental inconsistency in current magnetic field prescriptions in neutron star modeling and explores ways to address this issue.

Findings

Density-dependent magnetic field models violate Maxwell's equations.

The violation magnitude varies with different equations of state.

Some prescriptions can be corrected to satisfy Maxwell's equations.

Abstract

We show that the widely used density dependent magnetic field prescriptions, necessary to account for the variation of the field intensity from the crust to the core of neutron stars violate one of the Maxwell equations. We estimate how strong the violation is when different equations of state are used and check for which cases the pathological problem can be cured.