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 Quote by A.I. My question is threefold, the second is based on the premise that the first is true, and the third is based on the other two. 1. As relative velocity increases, mass also increases, correct? In this case, could you accelerate away from an object fast enough that its schwartzchild radius would be larger than the object, creating a black hole?
If the energy used to accelerate the object was already stored in the system to begin with, then that system was already a black hole to begin with. If the energy used to accelerate the object was added from some external source, then the system would become a black hole simply because you poured a massive amount of energy into it.

 Quote by A.I. 2. Would this object then collapse in upon itself so that if you slowed down to zero speed relative to the object, it would still be a black hole?
Kinetic energy is not "in" the moving object. Its "in" the relative motion of two or more objects. Consider that you cannot extract kinetic energy from an object that happens to be moving relative to you unless you use some machine to extract it, and that machine must connect to the object AND connect to a massive object stationary to you.

 Quote by A.I. 3. Will the outward acceleration of the universe ultimately result in the formation of black holes due to the very high velocity of objects relative to one another?
No, because of the previous answers.