The aim of the paper is to study weak gravitational lensing of quantum(perturbed) and classical lukewarm black holes(QLBHs and CLBHs respectively) in the presence of cosmological parameterΛ.We apply a numerical method to evaluate the deflection angle of bending light rays,image locationsθ of sample source β =-π/4,and corresponding magnifications μ.There are no obtained real values for Einstein ring locations θ_E(β = 0) for CLBHs but we calculate them for QLBHs.As an experimental test of our calculations,we choose mass M of 60 types of the most massive observed galactic black holes acting as a gravitational lens and study quantum matter field effects on the angle of bending light rays in the presence of cosmological constant effects.We calculate locations of non-relativistic images and corresponding magnifications.Numerical diagrams show that the quantum matter effects cause absolute values of the quantum deflection angle to be reduced with respect to the classical ones.The sign of the quantum deflection angle is changed with respect to the classical values in the presence of the cosmological constant.This means dominance of the anti-gravity counterpart of the cosmological horizon on the angle of bending light rays with respect to absorbing effects of 60 local types of the most massive observed black holes.Variations of the image positions and magnifications are negligible when increasing dimensionless cosmological constant ∈=(16ΛM^2)/3.The deflection angle takes positive(negative) values for CLBHs(QLBHs) and they decrease very fast(slowly) by increasing the closest distance x_0 of bending light ray and/or dimensionless cosmological parameter for sample giant black holes with0.001 < ∈ < 0.01.
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