Gravitational Lensing — Schwarzschild

Light passing near a massive body follows geodesics in curved spacetime. The Schwarzschild deflection angle is α = 4GM/c²b = 2r_s/b, where b is the impact parameter and r_s is the Schwarzschild radius. Stars behind the lens appear as arcs or Einstein rings.

Lens Parameters

Lens plane: center
Source plane: z = 2D
Observer: z = 0
r_s = px
Einstein R = px