Gravitational deflection of relativistic massive particles by Kerr black holes and Teo wormholes viewed as a topological effect

TL;DR

This paper introduces a novel method using optical metrics and the Gauss-Bonnet theorem to calculate the gravitational deflection angles of relativistic massive particles by Kerr black holes and Teo wormholes, highlighting their topological nature.

Contribution

It presents an alternative approach to compute deflection angles based on refractive indices and topological effects, applicable to rotating black holes and wormholes.

Findings

Exact deflection angles derived for Kerr black holes and Teo wormholes.

Revealed the topological nature of particle trajectories in curved spacetime.

Unified treatment of light and massive particle deflections using the Gauss-Bonnet theorem.

Abstract

We consider the problem of gravitational deflection of a propagating relativistic massive particles by rotating black holes (Kerr black holes) and rotating wormholes (Teo wormholes) in the weak limit approximation. In particular we have introduced an alternative way to calculate the deflection angle for massive particles based on the refractive index of the optical media and the Gauss-Bonnet theorem applied to the isotropic optical metrics. The refractive index governing the propagation of massive particles is calculated by considering those particles as a de Broglie wave packets. Finally applying the Gauss-Bonnet theorem leads to an exact result for the deflection angle in both geometries. Put in other words, the trajectory of light rays as well as the trajectory of massive particles in a given spacetime background can be viewed as a global spacetime effect, namely as a topological effect.