We present firstly equation of motion for the photon coupled to Weyl tensor in a Kerr black hole

spacetime and then study further the corresponding strong gravitational lensing. We find that black

hole rotation makes propagation of the coupled photons more complicated, which brings about some

new features for physical quantities including the marginally circular photon orbit, the deflection

angle, the observational gravitational lensing variables and the time delay between two relativistic

images. There is a critical value of the coupling parameter for existence of the marginally circular

photon orbit outside the event horizon, which depends on the rotation parameter of black hole

and the polarization direction of photons. As the value of coupling parameter is near the critical

value, we find that the marginally circular photon orbit for the retrograde photon increases with the

rotation parameter, which modifies a common feature of the marginally circular photon orbit in a

rotating black hole spacetime since it always decreases monotonously with the rotation parameter

in the case without Weyl coupling. Combining with the supermassive central object in our Galaxy,

we estimated the observables including time delays between the relativistic images in the strong

gravitational lensing as the photons couple to Weyl tensor.

# Boyer Center

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