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The unit vectors associated with a given point in a curved spacetime are not orthogonal to one another as they would be in a flat spacetime. This has the effect that motion along one axis couples into one or more other axis because the x,y,z,t coordinates are no longer independent of one another. In this case, the object at rest is still moving through time and because of the curvature of spacetime, this movement is coupled into the spatial dimensions producing gravity.