Neutrinos in curved spacetime: Particle mixing and flavor oscillations

We present a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, we analyze the nontrivial interplay between quantum field mixing and field quantization in curved space and derive new oscillation formulas. We compute the formulas explicitly in the spatially flat Friedmann--Lemaitre--Robertson--Walker metrics for universes dominated by a cosmological constant and by radiation. We evaluate the transition probabilities in the Schwarzschild black hole metric, and we show that the Hawking radiation affects the oscillations of neutrinos. We show that our results are consistent with those of previous analyses when the quantum mechanical limit is considered.