Strong gravitational lensing for the photons coupled to Weyl tensor in a Schwarzschild black hole spacetime

We have investigated the strong gravitational lensing for the photons coupled to Weyl tensor in a Schwarzschild black hole spacetime. We find that in the four-dimensional black hole spacetime the equation of motion of the photons depends not only on the coupling between photon and Weyl tensor, but also on the polarization direction of the photons. It is quite different from that in the case of the usual photon without coupling to Weyl tensor in which the equation of motion is independent of the polarization of the photon. Moreover, we find that the coupling and the polarization direction modify the properties of the photon sphere, the deflection angle, the coefficients in strong field lensing, and the observational gravitational lensing variables. Combining with the supermassive central object in our Galaxy, we estimated three observables in the strong gravitational lensing for the photons coupled to Weyl tensor.