Neutrino interaction with background matter in a non-inertial frame

We study Dirac neutrinos propagating in rotating background matter. First we derive the Dirac equation for a single massive neutrino in the non-inertial frame, where matter is at rest. This equation is written in the effective curved spacetime corresponding to the co-rotating frame. We find the exact solution of the Dirac equation. The neutrino energy levels for ultrarelativistic particles are obtained. Then we discuss several neutrino mass eigenstates, with a nonzero mixing between them, interacting with rotating background matter. We derive the effective Schrodinger equation governing neutrino flavor oscillations in rotating matter. The new resonance condition for neutrino oscillations is obtained. We also examine the correction to the resonance condition caused by the matter rotation. (AU)