Effect of the quintessential dark energy on weak deflection angle by Kerr-Newmann Black hole

TL;DR

This paper investigates how quintessential dark energy influences the weak gravitational lensing effect around Kerr-Newman black holes, providing new calculations and verifications of light deflection angles.

Contribution

It introduces a novel analysis of light deflection in Kerr-Newman black holes with quintessential dark energy using the Gauss-Bonnet theorem and null geodesic equations.

Findings

Deflection angle computed using Gauss-Bonnet theorem and geodesic equations agree.

Graphical analysis shows how deflection varies with impact parameter.

Results extend understanding of gravitational lensing in dark energy-influenced black hole spacetimes.

Abstract

In this work, we study the weak gravitational lensing in the background of Kerr-Newman black hole with quintessential dark energy. Initially, we compute the deflection angle of light by charged black hole with quintessential dark energy by utilizing the Gauss-Bnnet theorem. Firstly, we suppose the light rays on the equatorial plane in the axisymmetric spacetime. In doing so, we first find the corresponding optical metrics and then calculate the Gaussian optical curvature to utilize in Gauss-Bonnet theorem. Consequently, we calculate the deflection angle of light for rotating charged black hole with quintessence. Additionally, we also find the deflection angle of light for Kerr-Newman black hole with quintessential dark energy. In order to verify our results, we derive deflection angle by using null geodesic equations which reduces to the deflection angle of Kerr solution with the reduction of specific parameters. Furthermore, we analyze the graphical behavior of deflection angle $\Theta$ w.r.t to impact parameter $b$. Our graphical analysis retrieves various results regarding to the deflection angle by the Kerr-Newman black hole with quintessential dark energy.