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

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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.