We circular photon orbit for the retrograde photon

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.


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