  The interaction of neutrinos with gravitational fields in the weak field
regime at one loop to the leading order has been studied by Menon and
Thalappilil. They deduced some theoretical differences between the Majorana and
Dirac neutrinos. Then they proved that, in spite of these theoretical
differences, as far as experiments are concerned, they would be virtually
indistinguishable. We study the interaction of neutrinos with weak
gravitational fields to the second order (at two loops). We show that there
appear new neutrino gravitational form factors which were absent in the
first-order calculations, so from a theoretical point of view there are more
differences between the two kinds of neutrinos than in the first order, but we
show that likewise they are indistinguishable experimentally.
