Gravitational lensing by the hairy Schwarzschild black hole

Abstract

In this manuscript, we consider the hairy Schwarzschild black hole that evades the no-hair theorem. The hair is induced by an additional source from surroundings, such as dark matter, that has a constant energy-momentum tensor(EMT). 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 $\alpha$ but decreases with $\ell_0$. 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 $\ell_0=1$. With the help of the Gauss-Bonnet theorem, we briefly describe the weak gravitational lensing in the background of the hairy Schwarzschild black hole.