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The photon sphere
The knife-edge at 1.5 rs where gravity bends light into a circle — and why a black hole’s portrait is mostly shadow.
The dashed violet ring on the stage marks the photon sphere — the one distance from a black hole where gravity bends light’s path into a closed circle, so a photon can orbit the hole like a tiny moon.
In the river picture, a photon there aims about 35° upstream of sideways, its swim exactly cancelling the inflow. The balance is a knife edge, like a ball resting on the crest of a hill: a hair inside and it spirals down, a hair outside and it gets away. The long coral flashes that wrap the hole before falling in are skimming this ring — and the rules of escape pivot across it. Outside, any outward-moving flash gets free; inside, moving outward is no longer enough — only aims close to straight up clear the barrier.
That photograph is the photon sphere made visible. Light that crossed the ring never reached the telescope, so the dark patch is not the horizon itself but its lensed silhouette — about 2.6 horizon-radii across, the same critical aim that decides the fates on this stage. And the bright rim includes photons that circled the ring once or more before escaping to Earth.
Key terms
- photon sphere
- r = 1.5 rs, the only circular orbit light can hold. Unstable: any disturbance grows.
- impact parameter
- How far a ray’s straight-line aim misses the centre. Under the critical b꜀ ≈ 2.6 rs, the hole wins.
- the shadow
- The dark disc in a black-hole image — the photon sphere’s silhouette, 2.6× wider than the horizon.