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Nugatory

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Not right.To an observer moving fast enough, every object would seem to be a black hole, right?

A black hole forms or not according to how large the rest mass is, not the relativistic mass.

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This statement is common, but wrong. Moving objects have moreAccording to Special Relativity, objects moving fast have more mass than objects at rest.

Pop sci is more concerned wigh sounding cool and less concerned with clear communication, so has yet to catch up with that.

It can't. Gravity in relativity does not depend on relativistic mass, and people assuming it is basically Newtonian gravity with relativistic mass plugged in is one more reason to abandon the concept. The source term for gravity in relativity is the stress-energy tensor, which includes mass and other terms related to momentum and pressure. But they don't simply add to the mass in any naive way.How can an object both be a black hole and not be a black hole?

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You May like this FAQ from John Baez’s collectionNow if it were moving fast enough as well, it would gain enough mass density to become black hole. But to the observer moving in its frame of reference it would not.

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html