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

## TL;DR

This paper investigates how the hair on asymptotically flat charged black holes in Einstein-Maxwell-dilaton theory affects the deflection angle of light in weak gravitational lensing, considering both vacuum and plasma medium effects.

## Contribution

It provides an analytical study of the influence of black hole hair on photon deflection angles using Gauss-Bonnet theorem in Einstein-Maxwell-dilaton spacetime.

## Key findings

- Hair significantly affects the deflection angle in weak field limits.
- Plasma medium modifies the gravitational lensing effect.
- Analytical expressions for deflection angles are derived.

## 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.