Question: Show that there is exactly one radius at which a light beam can move in a circular orbit around a spherical black hole, and find

Show that there is exactly one radius at which a light beam can move in a circular orbit around a spherical black hole, and find this radius. Then show that the orbit is unstable, by showing that a tangential beam beginning at a slightly larger radius will spiral outward and never return, and a tangential beam beginning at a slightly smaller radius will spiral into the black hole.

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