  The strong gravitational field around a proto-neutron star can modify the
neutrino flavor transformations that occur above the neutrinosphere via three
General Relativistic (GR) effects: time dilation, energy redshift, and
trajectory bending. Depending on the compactness of the central object, the
neutrino self-interaction potential is up to three times as large as that
without GR principally due to trajectory bending which increases the
intersection angles between different neutrino trajectories, and time dilation
which changes the fluxes. We determine whether GR effects are important for
flavor transformation during the different epochs of a supernova by using
multi-angle flavor transformation calculations and consider a density profile
and neutrino spectra representative of both the accretion and cooling phases.
We find the GR effects are smaller during the accretion phase due to low
compactness of the proto-neutron star and merely delay the decoherence; the
neutrino bipolar oscillations during the cooling phase are also delayed due to
the GR effects but the delay may be more important because the delay occurs at
radii where it might alter the nucleosynthesis in the neutrino driven wind.
