Possibly simplistic question about massive moving objects

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Hi everyone. Can someone check my logic here please?

I think I have a pretty good grasp of the basics of special relativity, but I'm wondering about something. When a massive object approaches the speed of light, it's mass increases. So, as it gets closer and closer to the speed of light, it's mass approaches infinity. So it's gravitational force approaches infinity. Does this mean that any massive object going sufficiently near the speed of light effectively becomes a black hole?

I suspect that general relativity would have to be involved, but I don't have any real knowledge of that; I can only take that course in two years time!

Can anyone help me out, and/or point me towards a good source to explain?
 
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Consider 3 observers, A, B and C. Suppose that A sees B receeding very close to the speed of light, but C sees B receeding at a much lower speed. If objects could turn into BHs merely from relative velocity, then it's possible that A will see B become a BH, and C will not. This could lead to a causal paradox. It will definitely cause an argument between A and C.:smile:
 
Thanks, that clears things up!
 

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