Black Hole Geodesics

A Schwarzschild black hole rendered by the reused real-time lensing shader: the background star field is bent, the photon sphere glows as a ring, the shadow is a true black disc, and a Doppler-beamed accretion disc circles it. Below, an equatorial plane lets you fire test photons and massive particles whose geodesics are integrated from the exact orbit equation. The drama is the critical impact parameter b = 3 sqrt(3) M: a photon aimed just outside it loops the photon sphere and escapes, one just inside is captured. The effective potential V(r) shows why the innermost stable circular orbit sits at 6 M.