Higher order corrections to deflection angle of massive particles and light rays in plasma media for stationary spacetimes using the Gauss-Bonnet theorem

TL;DR

This paper extends the application of the Gauss-Bonnet theorem to compute higher order corrections to the deflection angles of light and massive particles in plasma media within stationary spacetimes, including Kerr black holes.

Contribution

It generalizes previous results to stationary spacetimes and introduces a method to calculate higher order deflection angle corrections for particles in plasma media.

Findings

Derived third-order corrections for deflection angles in Kerr spacetime.

Applied the Gauss-Bonnet theorem to plasma media in stationary spacetimes.

Showed the method's effectiveness for both light and massive particles.

Abstract

The purpose of this article is twofold. First, we extend the results presented in [Gabriel Crisnejo and Emanuel Gallo, Phys.Rev.D 97, 124016 (2018)] to stationary spacetimes. Specifically, we show that the Gauss-Bonnet theorem can be applied to describe the deflection angle of light rays in plasma media in stationary spacetimes. Second, by using a correspondence between the motion of light rays in a cold non magnetized plasma and relativistic test massive particles we show that this technique is not only powerful to obtain the leading order behavior of the deflection angle of massive/massless particles in the weak field regime but also to obtain higher order corrections. We particularize it to a Kerr background where we compute the deflection angle for test massive particles and light rays propagating in a non homogeneous cold plasma by including third order corrections in the mass and spin parameters of the black hole.