Circularly Polarized Light in Kerr Gravitational Field: Its Implication in Spin-Gravity Interaction

Abstract

Various calculations carried out in the past to understand the propagation of light in a rotating gravitational field (viz., Kerr field) are examined. For a plane-polarized light, it is observed that due to the effect of rotational gravitational field, the polarization vector of light gets rotated, with the amount of rotation independent from the frequency of the light. In the present work, using the formulations of geometrical optics, I try to find the implications of such findings, which seem to be very strange and give rise to violation of Lorentz Invariance and the Equivalence Principle, which are mostly not accepted by present-day physics. The analysis involves splitting plane-polarized light into left and right circularly polarized components, and then one finds that these two components (with a given frequency) travel with two different velocities in the Kerr field. Also, for an individual circularly polarized component, the velocity of propagation depends on the frequency of light. Assuming the two opposite directions of circularly polarized light to represent two opposite photon spin states, the line element for circularly polarized light is found to depend on the photon spin in addition to frequency. Additional calculations are made to estimate the propagation time delay between two circularly polarized components (with given frequency) between the source and observer at finite distances from the Kerr mass. Some typical estimates of this time delay are made for the Sun and one pulsar, so that in the future one can experimentally verify these results. For an individual circularly polarized component, time delay expressions are also derived for the propagation of light at two different frequencies. It has been found that circularly polarized light with higher frequency (energy) travels faster in a rotating gravitational field as compared to its lower frequency counterpart.