Gravitational lensing of massive particles in Schwarzschild gravity

Understand

Both massless light ray and objects with nonzero mass experience trajectory bending in a gravitational field.

• In this work the bending of trajectories of massive objects in a Schwarzschild spacetime and the corresponding gravitational lensing (GL) effects are studied.
• A particle sphere for Schwarzschild black hole (BH) is found with its radius a simple function of the particle velocity and proportional to the BH mass.
• A single master formula for both the massless and massive particle bending angle is found, in the form of an elliptic function depending only on the velocity and impact parameter.