Neutrinos propagating in curved spacetimes

TL;DR

This paper explores how massless neutrinos propagate in curved spacetimes, proposing a new framework that distinguishes between internal and spacetime transformations, and investigates implications for neutrino flavor oscillations.

Contribution

It introduces a novel approach to split neutrino spinors into particle and spacetime types, enhancing physical understanding and analyzing neutrino scattering in curved spacetimes, with a case study in Schwarzschild geometry.

Findings

Framework for separating internal and spacetime transformations

Worked example of neutrino propagation in Schwarzschild spacetime

Potential under-determinacy in flavoured Dirac-Weyl equation

Abstract

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.