Spinor Fields and Symmetries of the Spacetime

TL;DR

This paper investigates the behavior of spinor fields in black hole spacetimes, showing that their conserved currents align with Killing vectors at horizons and infinity, supported by tests on various solutions.

Contribution

It demonstrates that a general class of spinor fields have conserved currents approaching Killing vectors in black hole backgrounds, revealing a universal property.

Findings

Current approaches null on the horizon

Current approaches the time Killing vector at infinity

Results hold for various black hole solutions

Abstract

In the background of a stationary black hole, the "conserved current" of a particular spinor field always approaches the null Killing vector on the horizon. What's more, when the black hole is asymptotically flat and when the coordinate system is asymptotically static, then the same current also approaches the time Killing vector at the spatial infinity. We test these results against various black hole solutions and no exception is found. The spinor field only needs to satisfy a very general and simple constraint.