The way I understood general relativity is that there is no force of gravity but instead all object just move forward but the space they move through is distorted and that's why their trajectory seems to be different than a straight line. Now here is the question, if an object is not moving at all, i.e. it has no speed, does that mean that even though space is curved around them there is no speed to move the object towards the larger object?
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If an object is initially static from a larger object (assuming they have the same density), it will follow the geodesics in space-TIME. So the answer is yes because space-time is curved by the second object. This is why when you drop an object, it falls down to earth.
Jeanbaptiste Roux
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