Probing deflection angle inspired by weak field of specific black holes in non plasma and plasma field

The light bending (global and topological) phenomenon in the presence of black holes (BHs) will be examined by using the Gauss–Bonnet theorem (GBT) to understand the intricate physics . BHs inspired by non-minimal curvature-matter coupling with global monopole and dark matter halo, respectively, will be considered for analysing the above mentioned phenomenon. The deflection angle of light in the presence of weak field limits will be calculated by using well-known methodology called Gibbons–Werner. The effect of plasma medium will be assumed for analysing the bending of light phenomenon. We will also graphically examine the impact of different BH parameters on the computed bending angle. In the last, we also investigate the thermodynamic quantities such as sparsity and emission energy rate for both BHs.