Spacetime Route Dependence
Some gravitational arguments also suggest that the gravitational potential between two points in space, measured along an agreed spatial route, may depend on the amount of time that a test object takes to traverse the route (dependence on initial velocity). For an object moving between two positions, route dependence may apply not just to the spatial path but also to the spacetime path taken.
These arguments appear when we attempt to calculate the gravitomagnetic effects of the velocity of a body, and are more complicated.
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