Study of neutrino spin oscillations in a gravitational field with a differential equations method

TL;DR

This work tackles the problem of neutrino spin oscillations during gravitational scattering by a Kerr black hole. It develops an adaptive differential-equation framework that evolves both the neutrino trajectory in Kerr spacetime and the spin polarization, avoiding elliptic-integral calculations. The authors demonstrate that the differential-equation method yields $P_{LL}$ distributions that are in agreement with the traditional integral/Hamilton–Jacobi approach for two black-hole spin configurations, validating the method as a reliable cross-check. The approach sets the stage for incorporating accretion-disk physics and electroweak/electromagnetic interactions in future work, with numerical computations performed on the Govorun cluster.

Abstract

In this work, we employ Ordinary Differential Equation solution method to study neutrino spin oscillations in the case when they are gravitationally scattered off a rotating Kerr black hole. Previously, this problem involved the integral solution of the Hamilton-Jacobi equation. We analyze the consistency of these two methods.

Figures (1)

• Figure 1: Comparison of $PLL$'s obtained from integral and differential methods. (a) Upper neutrinos for $a = 0.02 M$, $\cos\theta = 0.01$, (b) Lower neutrinos for $a = 0.02 M$, $\cos\theta = 0.01$, (c) Upper neutrinos for $a = 0.98 M$, $\cos\theta = 0.01$, and (d) Lower neutrinos for $a = 0.98 M$, $\cos\theta = 0.01$,.