Weak Gravitational Lensing of quantum perturbed Lukewarm Black Holes and cosmological constant effect

Abstract: Aim of the paper is study weak gravitational lensing of quantum (perturbed) (QLBHL) and classical (CLBHL) Lukewarm black hole in presence of cosmological parameter $\Lambda$. We apply numerical method to evaluate deflection angle of bending light rays, images locations $\theta$ of sample source $\beta=-\frac{\pi}{4},$ and corresponding magnifications $\mu.$ There is not obtained real values for Einstein rings locations $\theta_E(\beta=0)$ for CLBHL but we calculate them for QLBHL. As experimental test of our calculations, we choose mass $M$ of 60 type of most massive observed galactic black holes as gravitational lens and study quantum matter fields effects on the angle of bending light rays in presence of the cosmological constant effects. We calculate locations of non-relativistic images and corresponding magnifications. Numerical diagrams show that the quantum matter effects cause to be reduce absolute values of the quantum deflection angle with respect to the classical ones. Sign of the quantum deflection angle is changed with respect to the classical values in presence of the cosmological constant. This means dominance of anti-gravity counterpart of the cosmological horizon on the bending light rays angle with respect to absorbing effects of local 60 type of observed most massive black holes. Variations of the image positions and magnifications are negligible by increasing dimensionless cosmological constant $\epsilon=\frac{16\Lambda M^2}{3}.$ Deflection angle takes positive (negative) values for CLBHL (QLBHL) and they decrease very fast (slow) by increasing closest distance $x_0$ of bending light ray and/or dimensionless cosmological parameter for sample giant black holes $0.001<\epsilon<0.01$.