Objects travel in straight lines through spacetime. Mass redefines “straight” and bends those lines towards it. Mass or no mass, an object’s path becomes curved.
An object won’t feel that curvature like you would if you were going around a bend in a car for example. As far as you’d be concerned, you’d still be going down a perfectly straight highway. No sideways forces ever get exerted on the object.
Black holes have enough mass that paths are curved right into it, creating an event horizon where there are no paths leading even light back out.
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