  It has been shown recently that the exchange of virtual neutrino pairs leads
to an unphysically large energy-density in neutron stars and white dwarfs,
unless neutrinos have a minimum mass, m > 0.4 eV. Here we consider the
possibility that the presence of trapped low-energy neutrinos can suppress the
exchange of virtual neutrino pairs, thereby avoiding a large energy-density
even for massless neutrinos. We show that a) there can be subvolumes in a
neutron star or white dwarf where neutrino-trapping does not take place, and
which can thus have an unphysically large energy density, and b) even in those
volumes where trapping does occur, the resulting suppression can be too small
to alter the conclusion that neutrinos must have a minimum mass.
