Optical properties of null geodesics emerging from dynamical systems

TL;DR

This paper investigates the optical behavior of null geodesics in various gravitational fields, deriving formulas for light deflection angles in different black hole metrics, enhancing understanding of gravitational lensing.

Contribution

It introduces new weak lensing formulas for Kerr black holes and generalizes deflection angle calculations to diverse solutions of Einstein's equations.

Findings

Derived a general deflection angle formula for Schwarzschild-Tangherlini metric.

Obtained a new weak lensing formula for Kerr black holes.

Explored light bending in Tomimatsu-Sato spacetime.

Abstract

We study optical metrics via null geodesics as a central force system, deduce the related Binet equation and apply the analysis to certain solutions of Einstein's equations with and without spherical symmetry. A general formula for the deflection angle in the weak lensing regime for the Schwarzschild-Tangherlini (ST) metric is derived. In addition, we obtain a new weak lensing formula for the deflection angle on the equatorial plane of a Kerr black hole (BH). We also explore the bending of light by considering the gravitational objects described by the Tomimatsu-Sato (TS) metric.