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We consider the problem of gravitational deflection of a propagatingrelativistic massive particles by rotating black holes (Kerr black holes) androtating wormholes (Teo wormholes) in the weak limit approximation. Inparticular we have introduced an alternative way to calculate the deflectionangle for massive particles based on the refractive index of the optical mediaand the Gauss-Bonnet theorem applied to the isotropic optical metrics. Therefractive index governing the propagation of massive particles is calculatedby considering those particles as a de Broglie wave packets. Finally applyingthe Gauss-Bonnet theorem leads to an exact result for the deflection angle inboth geometries. Put in other words, the trajectory of light rays as well asthe trajectory of massive particles in a given spacetime background can beviewed as a global spacetime effect, namely as a topological effect.

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