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For questions involving consideration of the shortest (or longest) path between two points in a curved space (e.g. a straight line between two points on the surface of a sphere such as the earth).
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In GR, how do particles know how to fall in instead of out of a gravitational well?
What you have noticed implies that both solutions (in and out) are acceptable physical solutions (that is, observing them would not be in violation of known principles). But which solution the particl …