Weak deflection angle by asymptotically flat black holes in Horndeski theory using Gauss-Bonnet theorem

TL;DR

This paper investigates gravitational lensing by asymptotically flat black holes within Horndeski theory using the Gauss-Bonnet theorem, analyzing photon deflection in weak fields and plasma media.

Contribution

It introduces a novel application of the Gauss-Bonnet theorem to compute photon deflection angles in Horndeski black hole spacetimes, including plasma effects.

Findings

Deflection angles calculated for black holes in Horndeski theory.

Impact of plasma medium on photon deflection analyzed.

Graphical results showing deflection variations with medium and parameters.

Abstract

The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss-Bonnet theorem to the optical geometry of asymptotically flat black holes and apply the Gibbons-Werner technique to achieve the deflection angle of photons in weak field limits. Subsequently, we manifest the influence of plasma medium on deflection of photons by asymptotically flat black holes in the context of Horndeski theory. We also examine the graphical impact of deflection angle on asymptotically flat black holes in the background of Horndeski theory in plasma medium as well as non-plasma medium.