Studying Gravitational Deflection of Light by Kiselev Black Hole via Homotopy Perturbation Method

TL;DR

This paper applies the homotopy-perturbation method to analytically approximate the gravitational deflection of light near a Kiselev black hole, demonstrating its effectiveness and deriving a series formula for the deflection angle.

Contribution

It introduces the use of homotopy-perturbation method for solving null-geodesics around Kiselev black holes, providing a new analytical approach in gravitational lensing studies.

Findings

HPM yields acceptable solutions for null-geodesics in black hole spacetimes.

Derived a series formula for the deflection angle applicable to any accuracy.

Validated HPM approach with Schwarzschild and Reissner-Nordström black holes.

Abstract

In this paper, the homotopy-perturbation method (HPM) is applied to obtain approximate analytical solutions for the gravitational deflection of light in General Relativity near Schwarzschild black hole surrounded by quintessence (Kiselev black hole). In order to demonstrate that HPM is able to yield acceptable solutions for the null-geodesics with easily computable terms, the HPM is tested for the simple examples of spherically symmetric spacetimes such as Schwarzschild and Reissner-Nordstr\"{o}m black holes. After that, the null-geodesics of light passing the vicinity of Kiselev black hole are studied via the HPM in two particular cases regarding the equation of state parameter of quintessence. In addition, a formula for the angle of deflection has been obtained via HPM in the form of a series which allows to calculate the angle with any accuracy without requirement of its smallness.