Massive Object Paradox: Traveling Near Speed of Light?

[em370]

If a object with mass and density just below what is required to form a black hole is traveling near the speed of light relative to an observer, its mass should appear to increase, and its length contract, to the observer. The objects mass and density will increase pass the threshold necessary to form a black hole. To the observer the object should collapse and form a black hole, while from the object's perspective it is unchanged. Does someone have a resolution to this paradox?

 

[PeterDonis]

The resolution is that a black hole does not form, because in GR, the source of gravity is not "mass" but the stress-energy tensor. The stress-energy tensor transforms when you change frames such that observables, like whether or not a black hole forms, remain invariant.

See here for a brief discussion:

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