Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment

TL;DR

This paper uses the Gauss-Bonnet theorem to analyze gravitational lensing effects on light and massive particles in plasma media within static, spherically symmetric spacetimes, providing a unified geometric approach.

Contribution

It introduces a novel geometric framework applying the Gauss-Bonnet theorem to both light and massive particles in plasma, unifying their gravitational deflection analysis.

Findings

Derived deflection angles for light in plasma with various density profiles.

Computed gravitational deflection of massive particles in weak fields.

Demonstrated the applicability of the geometric method to different spacetime symmetries.

Abstract

We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with the same symmetries. The possibility of using the theorem follows from a correspondence between timelike curves followed by light rays in a plasma medium and spatial geodesics in an associated Riemannian optical metric. A similar correspondence follows for massive particles. For some examples and applications, we compute the deflection angle in weak gravitational fields for different plasma density profiles and gravitational fields.