We calculate the minimum distance at which one may approach a black hole in a free flyby. It corresponds to r=4m for the Schwarzschild black hole for a probe that was non-relativistic at infinity. The problem is formulated in a way that is useful for teaching introductory general relativity.

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Those readers who are familiar with the concept of the Killing vectors may apply here more general reasoning. The scalar products of the Killing vectors t,φ and the probe four-velocity are conserved along the geodesic.
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