  Propagation of fermions in curved space-time generates gravitational
interaction due to coupling of its spin with space-time curvature connection.
This gravitational interaction, which is an axial-four-vector multiplied by a
four gravitational vector potential, appears as CPT violating term in the
Lagrangian which generates an opposite sign and thus asymmetry between the
left-handed and right handed partners under CPT transformation. In the case of
neutrinos this property can generate neutrino asymmetry in the Universe. If the
background metric is of rotating black hole, Kerr geometry, this interaction
for neutrino is non-zero. Therefore the dispersion energy relation for neutrino
and its anti-neutrino are different which gives rise to the difference in their
number densities and neutrino asymmetry in the Universe in addition to the
known relic asymmetry.
