Minimum size for a black hole to capture a photon

Minimum size for a black hole to capture a photon

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If a photon is moving past a black-hole, what is the minimum size of the black-hole that will capture the photon and prevent the photon from going onto orbit around the mass? Do black-holes exist that have a stream of photons orbiting them?

There isn't really a minimum size. All black holes have an event horizon from which nothing, not even light can escape. The (Schwarzschild) radius of this event horizon is 3km for a black hole of a solar mass and scales linearly with mass. There is a region just outside the event horizon called the photon sphere, within which light can briefly orbit the black hole, but not in a stable fashion. It will either fly off in some other direction or spiral into the black hole.

You can check out this Physics SE question to see a derivation of the impact parameter (the effective radius at which light will be absorbed) and you will see that it is a small numerical factor ($sqrt{27/4}$ for a non-rotating black hole) times the Schwarzschild radius (the event horizon of a non-rotating black hole), which is indeed proportional to the black hole mass.

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