  We show that under gravity the effective masses for neutrino and antineutrino
are different which opens a possible window of neutrino-antineutrino
oscillation even if the rest masses of the corresponding eigenstates are same.
This is due to CPT violation and possible to demonstrate if the neutrino mass
eigenstates are expressed as a combination of neutrino and antineutrino
eigenstates, as of the neutral kaon system, with the plausible breaking of
lepton number conservation. In early universe, in presence of various lepton
number violating processes, this oscillation might lead to
neutrino-antineutrino asymmetry which resulted baryogenesis from the B-L
symmetry by electro-weak sphaleron processes. On the other hand, for Majorana
neutrinos, this oscillation is expected to affect the inner edge of neutrino
dominated accretion disks around a compact object by influencing the neutrino
sphere which controls the accretion dynamics, and then the related type-II
supernova evolution and the r-process nucleosynthesis.
