Optical properties of a Brane-World black hole as photons couple to the Weyl tensor

TL;DR

This paper studies how photons coupled to the Weyl tensor behave around a Brane-World black hole, revealing a double shadow phenomenon and analyzing the influence of various parameters on the black hole's optical appearance.

Contribution

It introduces the analysis of photon propagation coupled to the Weyl tensor in a Brane-World black hole, highlighting the double shadow effect and finite-distance light deflection corrections.

Findings

Existence of a double shadow due to polarization-dependent photon paths.

Effects of parameters $eta$, $eta$, and $eta$ on the shadow's size and shape.

Finite-distance corrections to light deflection angles in this spacetime.

Abstract

In this article, we have investigated the equations of motion of the photons coupled to Weyl tensor by the geometric optics approximation and the corresponding shadow in a Brane-World black hole spacetime. It is shown that there exists a double shadow for a black hole since the coupling photons with different polarization directions propagate along different paths in the spacetime. Furthermore, we discuss the effects of the metric parameter $\alpha$ related to the cosmological constant, X-cold dark matter parameter $\beta$ and the coupling parameter $\lambda$ on the umbra (the overlap region of the double shadow) and the penumbra. We also obtain the finite-distance corrections to the deflection angle of light in the Brane-World black hole spacetime as the photons coupled to Weyl tensor by using a recent geometric method.