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