Temporal Instability Enables Neutrino Flavor Conversions Deep Inside Supernovae

We show that a self-interacting neutrino gas can spontaneously acquire a non-stationary pulsating component in its flavor content, with a frequency that can exactly cancel the "multi-angle" refractive effects of dense matter. This can then enable homogeneous and inhomogeneous flavor conversion instabilities to exist at large neutrino and matter densities, where the system would have been stable if the evolution were strictly stationary. Large flavor conversions very close to a supernova core may become possible via this novel mechanism, with important consequences for the explosion dynamics and nucleosynthesis, as well as for neutrino observations of supernovae