Effect of the hair on deflection angle by asymptotically flat black holes in Einstein-Maxwell-dilaton theory

In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of a dilaton potential. We study the weak gravitational lensing in the spacetime of a hairy black hole in the Einstein-Maxwell theory with a nonminimally coupled dilaton and its nontrivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $\ensuremath{\gamma}$. For this purpose, by using the Gauss-Bonnet theorem, we obtain the deflection angle of the photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investigate the impact of the plasma medium on weak gravitational lensing by an asymptotically flat charged hairy black hole with a dilaton potential. Our analyses show the effect of the hair on the deflection angle in weak-field limits.

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