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Gravitational lensing by the hairy Schwarzschild black hole

May 12, 2022

14 pages

e-Print:

2205.06052 [gr-qc]

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Abstract: (arXiv)

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.

Note:

14 pages with fig. and tables. arXiv admin note: text overlap with arXiv:gr-qc/0208075, arXiv:1910.02030 by other authors

black hole: Schwarzschild
gravitation: lens
tensor: energy-momentum
black hole: hair
background
dark matter
impact parameter
photon: deflection
deflection: angular dependence

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