  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.
