The microscopic structure of the inner crust of neutron stars is generally studied in the framework of local energy density functionals (EDF). Here, we discuss other possible frameworks, either based on non- relativistic EDF which are fully non-local, or covariant EDF of the relativistic mean field (RMF) type. These other approaches must be more widely used in the context of neutron stars in order to gain confidence in predicting general trends.
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