Affine perturbation series of the deflection angle of a ray near the photon sphere of a Reissner-Nordstr\"{o}m black hole

TL;DR

This paper analyzes the deflection angle of light near a Reissner-Nordström black hole's photon sphere using an affine perturbation series, finding the 0th order provides better accuracy than traditional strong deflection limit methods.

Contribution

It introduces the use of an affine perturbation series for more accurate calculation of light deflection near black holes, improving upon existing strong deflection limit approaches.

Findings

0th order affine perturbation series outperforms the strong deflection limit in accuracy.

Comparison shows the 1st order improves the approximation but is less accurate than the 0th order.

The study suggests refining strong deflection limit analysis with the 0th order affine series.

Abstract

We investigate the affine perturbation series of the deflection angle of a ray near the photon sphere of an extreme Reissner-Nordstr\"{o}m black hole. We compare the 0th and 1st orders of the affine perturbation series with the deflection angle in a strong deflection limit. We conclude that the 0th order of the affine perturbation series is more accurate than the deflection angle in the strong deflection limit and that we should improve a strong-deflection-limit analysis by using the 0th order of the affine perturbation series.