Null geodesics in Schwarzschild spacetime. The photon sphere at r=3M and shadow radius r_shadow=3√3 M ≈ 5.196 M.
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In Schwarzschild geometry, photon trajectories satisfy d²u/dφ² + u = 3Mu² (u=1/r).
The unstable photon orbit at r=3M (the photon sphere) defines the shadow boundary.
Photons with impact parameter b < b_crit = 3√3 M are captured; the shadow appears as a dark disk of radius ≈ 5.196 M as seen from infinity.
The orange glow models accretion disk emission at r = 3M–6M (ISCO at r=6M).