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

摘要

We present first the equation of motion for the photon coupled to a 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 the black hole and the polarization direction of the photons. As the value of the coupling parameter nears 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. Modeling the supermassive central object in our Galaxy as a Kerr black hole, we estimate the numerical values of the observables including time delays between the relativistic images in the strong gravitational lensing of the photons coupled to Weyl tensor.