Spin-orbit couplings of quantum fields in Schwarzschild spacetime

TL;DR

This paper investigates gravitational spin-orbit couplings of massless Dirac and photon fields in Schwarzschild spacetime using quantum field theory, revealing energy-level splittings and polarization effects related to black hole Hawking radiation.

Contribution

It presents a unified quantum field theory analysis of spin-orbit couplings for massless particles in Schwarzschild spacetime, without using Foldy-Wouthuysen transformation.

Findings

Energy-level splittings are identical for particles with the same momentum.

Massless particles from Hawking radiation are partially polarized.

Polarization depends on the momentum orientation relative to the black hole.

Abstract

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.