The origin of any coordinate system is equivalently a center for a nonzero force. When the magnitude of this force becomes identically zero then and only then does the coordinate system cease to exist. Hence coordinate free environment is the same as a force free environment.
In regard to gravitational field, zero gravity means weightlessness (forceless) but not necessarily zeros mass. However, the infinitesimal region of mass field could logically support two centers and these likewise described the left and the right system. Furthermore, these distinct systems (left and right) described two distinct local motions, clockwise and counterclockwise, with analogy to positive and negative spin of elementary particles.


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