I appreciate that you?re trying to figure this out, but there are
some things you evidently don?t yet understand.
First off, it?s not the acceleration which is inducing the supposed
increase in mass. It?s just the relative velocity.
Second, there isn?t really any increase in mass with velocity.
That?s nowadays an obsolete interpretation of special relativity. All
the effects which were once attributed to changes in mass are
understandable via time dilation.
A black hole can have any mass, large or small- if it?s contained
within its own Schwartzchild Radius. Your body could be a black hole,
if it were squashed small enough. The Sun isn?t a black hole because
its Schwartzchild Radius is a lot smaller than the Sun currently is.
So yes, if you turned a knob and increased the strength of gravity
sufficiently, everything could be made into black holes.
It?s not necessarily true that any two colliding particles have
much likelihood of approaching close enough to form a black hole. For
instance, suppose two deuterons smash into each other. (A deuteron is
a heavy hydrogen nucleus, one proton & one neutron.) As they get
close, the protons? mutual electrical repulsion accelerates them away
from each other. Once they do get close enough, the short-range gluon
force can equal the electrical repulsion, and the two deuterons will
just lock together to form a helium nucleus. But it?s hard enough just
to get them close enough to undergo nuclear fusion. Once they lock at
short range, the gluon force is at equilibrium with the electrical
force. It then becomes incredibly hard to press them even further
together. Getting them close enough to form a black hole isn?t
something which will happen very casually.
Regarding increasingly massive elements becoming black holes, it
won?t happen. Keep in mind that, even as the mass-number of an element
rises, so also does the diameter of the nucleus. It?s always larger
than its own Schwartzchild Radius. Consider a neutron star. It?s a
very large-scale atomic nucleus, a mass of neutrons. Yet it doesn?t
spontaneously collapse into a black hole.
Incidentally, regarding the first sentence in your post, about the
?new particle accelerator?, this refers to an experiment a year or two
back at Brookhaven, in which heavy ions were collided into targets.
What essentially happened was very interesting.
In general relativity there?s an idea called the ?equivalence
principle?. Roughly speaking, any two equally accelerated frames of
reference are considered equivalent. As I stand on the ground, I?m
immersed in Earth?s gravitational field. I am accelerated downward via
gravity. I?m also accelerated upward due to the electrical repulsion
of the outer orbital electrons in the surface atoms of both my feet
and the soil.
So what if a charged particle is smashed into an equally charged
target at high velocity? It gets very HIGHLY accelerated by the rapid
interaction in the brief collision. This very large acceleration is
equivalent to the particle being immersed in a strong gravitational
field. If the accelerator gets the particle up to a high enough speed,
and it loses that speed fast enough in the collision, it?s like
creating the gravitational environment near a tiny black hole. So what
happens in the near neighborhood of small black holes? They emit
Hawking Radiation. This is what the researchers speculate that they
observed in their experiment, Hawking Radiation.