Maxwell equation violation by density dependent magnetic fields in   neutron stars
  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. 
D\'ebora P. Menezes and Marcelo D. Alloy
astro-ph.HE