Eur. Phys. J. Plus (2023) 138: 86
https://doi.org/10.1140/epjp/s13360-023-03650-w

Regular Article

Strong gravitational lensing in hairy Schwarzschild background

¹ Chandernagore College, Chandernagore, Hooghly, West Bengal, India
² Durgapur Government College, 713214, Durgapur, Burdwan, West Bengal, India

^b anisur@associates.iucaa.in, manisurn@gmail.com

Received: 11 September 2022
Accepted: 31 December 2022
Published online: 25 January 2023

Abstract

We consider the hairy Schwarzschild black hole that evades the no-hair theorem. The hair is induced by additional sources from the surroundings, namely dark matter, that has a constant energy-momentum tensor (EMT). Hair parameter was designated by ${\ell }_0$. We study the strong gravitational lensing of light in the background of the hairy Schwarzschild black hole. We observe that the lensing coefficient $\overline{a}$ increases with deviation parameter $\alpha$, but decreases with primary hair ${\ell }_0$. The opposite effect is observed for the lensing coefficient $\overline{b}$ and the impact parameter $b_m$. We also notice that the angular position ${\theta }_{\infty }$ decreases with $\alpha$ but increases with ${\ell }_0$, whereas the angular separation s increases with $\alpha$ and decreases with ${\ell }_0$. For all parameters mentioned, we regain their values for the Schwarzschild black hole whenever we put either $\alpha =0$ or take the limit ${\ell }_0\to 2M$. With the help of the Gauss-Bonnet theorem, we briefly describe the weak gravitational lensing in the background of the hairy Schwarzschild black hole.