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The (1, 0)+(0, 1) representation of the group SL(2, C) provides asix-component spinor equivalent to the electromagnetic field tensor. By meansof the (1, 0)+(0, 1) description, one can treat the photon field in curvedspacetime via spin connection and the tetrad formalism, which is of greatadvantage to study the gravitational spin-orbit coupling of photons. Once thegravitational spin-orbit coupling is taken into account, the traditional radiusof the circular photon orbit in the Schwarzschild geometry should be replacedwith two different radiuses corresponding to the photons with the helicities of+1 and -1, respectively. Owing to the splitting of energy levels induced by thespin-orbit coupling, photons (from Hawking radiations, say) escaping from aSchwarzschild black hole are partially polarized, provided that their initialvelocities possess nonzero tangential components.

The effect of gravitational spin-orbit coupling on the circular photon orbit in the Schwarzschild geometry