Deflection of Massive Spin-$\frac{1}{2}$ Particles around Kerr Black Hole

TL;DR

This paper explores how polarized spin-1/2 particles, like neutrinos, deflect around Kerr black holes to potentially measure their mass, using quantum equations to identify spin effects and propose new bounds on neutrino mass.

Contribution

It introduces a method to analyze spin-1/2 particle deflection around Kerr black holes using a quantum Dirac equation, linking intrinsic spin to the MPD equation, and suggests a new approach to estimate neutrino mass.

Findings

Corrections >10^{-12} for 1 eV/c^2 mass particles around solar mass black holes.

Quantum spin effects can be used to test neutrino mass bounds.

The MPD equation applies to particles' intrinsic quantum spin.

Abstract

The exact measurement of neutrino mass remains a longstanding issue. So far, there has been much success in providing an upper bound for the neutrino rest mass, both theoretically and experimentally. In this work, by exploring the critical radius of a beam of polarized quantum spin-$\frac{1}{2}$ particle deflecting around a classical Kerr black hole, we attempt to provide an additional testing ground for neutrino mass, as well as the mass of other proposed ultra-light particles yet to be determined. Notably, the quantum Dirac equation is used to derive a MPD-like equation satisfied by the polarized beam of massive spin-$\frac{1}{2}$ particles and identify the effective spin in the spin tensor with the particle's intrinsic quantum spin, confirming the previous theoretical result that the MPD equation can be in fact applied to particles' intrinsic spin. The result of this work shows that corrections of relative magnitude $>10^{-12}$ can be achieved for spin-$\frac{1}{2}$ particles with rest mass equal to $1 eV/c^2$ deflecting around a solar mass Kerr black hole. Although highly theoretical, a new method of extracting the lower bound for the neutrino mass individually is also proposed due to the behavior of the quantum spin correction.