Effect of the Dilaton Field on Deflection Angle of Massive Photons by Black Holes in Einstein-Maxwell-Dilaton-Axion Theory

In this paper, we argue that one can calculate the weak deflection angle in the background of Einstein-Maxwell-Dilaton-Axion black hole using the Gauss-Bonnet theorem. To support this, the optical geometry of the black hole with the Gibbons-Werner method are used to obtain the deflection angle of light in the weak field limits. Moreover, we investigate the effect of a plasma medium on deflection of light for a given black hole. Because of dilaton and axion are one of the candidate of the dark matter, it can give us a hint on observation of dark matter which is supported the black hole. Hence we demonstrate the observational viability via showing the effect of the dark matter on the weak deflection angle.