No birefringence in Einstein's gravity

Einstein's theory predicts that, massive test particles with non-zero spin or angular momentum, in an external gravitation field, follow geodesics which depend upon the orientation of the spin-angular momentum . It has been claimed that such an effect also holds for photons i.e. photons with different helicities follow different geodesics in the gravitational field of a rotating body and would give rise to a polarisation dependent deflection of light passing in the vicinity of the sun or a polarisation dependent time delay of pulsar signals . We show here that contrary to earlier claims , in Einstein's gravity there is no birefringence and photons follow null geodesics irrespective of polarisation. Thus if gravitational birefringence is ever observed experimentally it would be a signal of new physics beyond Einstein's gravity