rest mass/relativistic mass question

I was thinking about something and got confused so I thought I will
post it here and hopefully someone more knowledgeable than me can clear
the confusion.

As a thought experiment, suppose, we are accelerating a proton in a
large accelerator (as large as you need it to be). It will continuously
gain mass/energy. Will a time come when it has gained sufficient mass
energy to form a black hole? If not why not?

If yes, then what happens to an observer who is always at rest relative
to the proton? To that observer nothing is happening but then suddenly
the proton turns into a hole? Isn't physics seemingly violated for that
observer?

thanks for any clarification.

.

Relevant Pages

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