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

TL;DR

This paper investigates how photons coupled to the Weyl tensor behave in Kerr black hole spacetimes, revealing complex effects on gravitational lensing and photon orbits influenced by black hole rotation and coupling parameters.

Contribution

It introduces the equations of motion for Weyl-coupled photons in Kerr spacetime and analyzes their impact on gravitational lensing and photon orbits, highlighting new features due to coupling and rotation.

Findings

Black hole rotation complicates photon propagation with Weyl coupling.

Existence of a critical coupling value for photon orbits outside the event horizon.

Near the critical coupling, the photon orbit behavior differs from the standard Kerr case.

Abstract

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 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.