The precession of particle spin in spherical symmetric spacetimes

TL;DR

This paper investigates the precession of particle spins in spherical spacetimes, deriving a general precession equation, analyzing massless and massive particles, and revealing how spin behavior depends on spacetime properties and particle velocity.

Contribution

It derives a spin precession equation applicable to both massless and massive particles in spherical spacetimes, extending previous analyses and clarifying spin behavior during backward scattering.

Findings

Spin is reversed after backward scattering for massless particles.

In Schwarzschild spacetime, spin precession depends on deflection angle for slow particles.

In Reissner-Nordström spacetime, spin precession also depends on black hole charge.

Abstract

In this work, we will explore the precession of particle spins in spherical spacetimes. We first argue that the geometrical optics (WKB) approximation is insufficient, due to the absence of a glory spot in the backward scattering of massless particles, making an analysis of spin precession necessary. We then derive the precession equation assuming the spin is parallel transported, which is supported by the sub-leading order of the WKB approximation. The precession equation applies to both massless and massive particles. For particles moving at the speed of light, we show that spin is always reversed after backward scattering in any spherically symmetric spacetime, confirming the absence of a glory spot for massless particles. Finally, we solve the precession equation for Schwarzschild and Reissner-Nordstr\"om spacetimes and discuss the spin precession of massive particles, particularly in the non-relativistic limit. We find that, in Schwarzschild spacetime, the spin precession for particles moving with very small velocities compared to the speed of light depends only on the deflection angle, while in Reissner-Nordstr\"om spacetime, it also depends on the black hole charge, as revealed by the expansion derived from the strong lensing approximation.