No birefringence in Einstein’s gravity

Einstein’s theory predicts that, massive test particles with nonzero spin or angular momentum, in an external gravitation field, follow geodesics which depend upon the orientation of the spin-angular momentum [1]. It has been claimed [2] 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. If such an effect were to exist it would result in a polarisation dependent deflection of light passing in the vicinity of the sun [3] or a polarisation dependent time delay of pulsar signals [4]. We show here that contrary to earlier claims [2], 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 [5].