  In Schwarzschild spacetime, the gravitational spin-orbit couplings of the
massless Dirac field and the photon field can be studied in a unified way. In
contrary to the previous investigations presented mainly at the
quantum-mechanical level, our work is presented at the level of quantum field
theory without resorting to the Foldy-Wouthuysen transformation. If massless
Dirac particles and photons have the same momentums, their energy-level
splittings due to the gravitational spin-orbit couplings are the same. Massless
Dirac particles and photons coming from the Hawking radiations are partially
polarized as long as their original momentums are not parallel to the radial
direction of a Schwarzschild black hole.
