Maxwell Equation Violation by Density Dependent Magnetic Fields in Neutron Stars

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. We then propose a simple solution that allows for the usual prescriptions to be used without violating a fundamental equation of physics.