# Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole

• The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole. Here, we have extended the prior work of Chen and Jing (S. Chen and J. Jing, JCAP, 10: 002 (2015)) for a Schwarzschild black hole to a Kiselev black hole. For this purpose, the equation of motion for the photons coupled to the Weyl tensor, null geodesic, and equation of photon sphere in a Kiselev black hole spacetime have been formulated. It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor, but also on the polarization direction of the photons. There is a critical value of the coupling parameter, $\alpha$ , for the existence of the marginally circular photon orbit outside the event horizon, which depends on the parameters of the black hole and the polarization direction of the photons. Further, the polarization directions of the coupled photons and the coupling parameter, $\alpha$; both modify the features of the photon sphere, angle of deflection, and functions $(\bar{a}$ and $\bar{b})$ owing to the strong gravitational lensing in the Kiselev black hole spacetime. In addition to this, the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.

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G. Abbas, Asif Mahmood and M. Zubair. Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole[J]. Chinese Physics C. doi: 10.1088/1674-1137/44/9/095105
G. Abbas, Asif Mahmood and M. Zubair. Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole[J]. Chinese Physics C.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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## Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole

###### Corresponding author: M. Zubair, drmzubair@cuilahore.edu.pk
• 1. Departmentof Mathematics, The Islamia University of Bahwalpur, Pakistan
• 2. Department of Mathematics, COMSATS University, Islamabad, Lahore Campus, Pakistan

Abstract: The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole. Here, we have extended the prior work of Chen and Jing (S. Chen and J. Jing, JCAP, 10: 002 (2015)) for a Schwarzschild black hole to a Kiselev black hole. For this purpose, the equation of motion for the photons coupled to the Weyl tensor, null geodesic, and equation of photon sphere in a Kiselev black hole spacetime have been formulated. It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor, but also on the polarization direction of the photons. There is a critical value of the coupling parameter, $\alpha$ , for the existence of the marginally circular photon orbit outside the event horizon, which depends on the parameters of the black hole and the polarization direction of the photons. Further, the polarization directions of the coupled photons and the coupling parameter, $\alpha$; both modify the features of the photon sphere, angle of deflection, and functions $(\bar{a}$ and $\bar{b})$ owing to the strong gravitational lensing in the Kiselev black hole spacetime. In addition to this, the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.

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