  The observation of several neutron stars in the center of supernova remnants
and with significantly lower values of the dipolar magnetic field than the
average radio-pulsar population has motivated a lively debate about their
formation and origin, with controversial interpretations. A possible
explanation requires the slow rotation of the proto-neutron star at birth,
which is unable to amplify its magnetic field to typical pulsar levels. An
alternative possibility, the hidden magnetic field scenario, considers the
accretion of the fallback of the supernova debris onto the neutron star as
responsible for the submergence (or screening) of the field and its apparently
low value. In this paper we study under which conditions the magnetic field of
a neutron star can be buried into the crust due to an accreting, conducting
fluid. For this purpose, we consider a spherically symmetric calculation in
general relativity to estimate the balance between the incoming accretion flow
and the magnetosphere. Our study analyses several models with different
specific entropy, composition, and neutron star masses. The main conclusion of
our work is that typical magnetic fields of a few times 1e12 G can be buried by
accreting only 1e-3 - 1e-2 solar mass, a relatively modest amount of mass. In
view of this result, the Central Compact Object scenario should not be
considered unusual, and we predict that anomalously weak magnetic fields should
be common in very young (< few kyr) neutron stars.
