Special relativity tells us that a fast-moving object with sufficient speed will appear more massive that it would at rest relative to an observer. Since the strength of an object's gravitational field is proportional to its mass, wouldn't a fast-moving object also appear to the observer to have a stronger gravitational field? How would this manifest itself to an observer at rest in terms of it's gravitational interaction with other nearby objects and with light?
As a thought experiment, I am imagining two very fast moving objects moving in tandem along a straight line, separated by a short distance. They would appear to be much more massive to an observer at rest. Yet relative to one another, the objects are near motionless. Could an observer at rest measure a stronger gravitational field between the two fast moving objects than an observer riding along with them?
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