Weak gravitational lensing by multi horizons black hole

We investigate the weak gravitational lensing caused by multi horizon black hole (MHBH) on light. Using the Gauss-Bonnet theorem, which demonstrates that light bending is a topological and global phenomenon, we are able to deduce the deflection angle of light in the weak field limits. First, we use the Gauss-Bonnet theorem to estimate the Gaussian optical curvature and determine the MHBH deflection angle for spherically balanced spacetime. Further, we evaluate the deflection angle of light within the plasma medium framework. Likewise, the impact of plasma and the non-plasma medium clearly illustrate the dynamics of the deflection angle by multi horizons black hole. Keywords: Weak gravitational lensing; deflection angle; Gauss-Bonnet theorem.