Deflection Angle of Kazakov-Solodukhin Black Hole in Quintessence Using Homotopy Perturbation Method

This study uses the Homotopy Perturbation Method, which provides a systematic approach to solving non-linear differential equations occurring in the problem. Here, the homotopy perturbation method is applied to find the gravitational deflection of light of the Kazakov-Solodukhin-Kiselev black hole using the concept of weak gravitational lensing. To validate this method and its effectiveness in providing an accurate and computationally efficient solution for the Kazakov-Solodukhin black hole, this method has been applied to the metric. The equation of state parameter \(\omega \) is set for a specific case to account for the presence of quintessence, and the deflection angle is plotted for various cases, explaining the behavior of light under dependencies. The results show that the quintessence parameter (c) increases the deflection angle, thus enhancing the gravitational lensing and larger values of the distortion parameter (a), reduces the deflection angle with smaller values of a, leading to a sharper transition of deflection angle.