Strong gravitational field time delay for photons coupled to Weyl tensor in a Schwarzschild black hole

We analyze strong gravitational field time delay for photons coupled to the Weyl tensor in a Schwarzschild black hole. By making use of the method of strong deflection limit, we find that these time delays between relativistic images are significantly affected by polarization directions of such a coupling. A practical problem about determination of the polarization direction by observations is investigated. It is found that if the first and second relativistic images can be resolved, the measurement of time delay can more effectively improve detectability of the polarization direction.