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

Abstract

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

12 pages, Accepted for publication in Physical Review D (https://journals.aps.org/prd/accepted/e6073Q42Sfd1fc2763f48f75991d27803414417d9)