Neutrinos propagating in curved spacetimes

In the Dirac-Weyl equation that describes massless neutrino propagation in the minimal Standard Model, the ($2\times 2$ equivalence of the) gamma matrices convert Weyl spinors into spacetime tensors, and vice versa. They can thus be regarded as amalgamations of three different types of mappings, one that connects particle spinors directly forming representations to internal gauge symmetries to their spacetime counterparts that are embodied by null flags, another that translates the spacetime spinors into their corresponding tensors expressed in an orthonormal tetrad, and finally a purely tensorial transformation into the coordinate tetrad. The splitting of spinors into particle and spacetime varieties is not usually practised, but we advocate its adoption for better physical clarity, in terms of distinguishing internal and spacetime transformations, and also for understanding the scattering of neutrinos by spacetime curvature. We construct the basic infrastructure required for this task, and provide a worked example for the Schwarzschild spacetime. Our investigation also uncovers a possible under-determinacy in the flavoured Dirac-Weyl equation, which could serve as a new incision point for introducing flavour oscillation mechanisms.