I read recently that a new particle accelerator had a minuscule chance
of creating a black hole. Now, I know that if a particle accelerator
accelerates a particle fast enough, it should acquire enough mass to
become a black hole. But, the moment it stops accelerating, it'd lose
that mass and stop being a black hole. So, the only way for the
particle accelerator to actually create a permanent black hole would
be for it to accelerate it fast enough such that it became a black
hole and sucked in enough other mass past its Schwarzschild radius so
that it acquired enough non-temporary mass to remain a black hole once
it stopped accelerating.

That's correct isn't it?

Now, here is the part that I'm confused about. Supposedly it's
possible to have non-accelerating black holes that have less mass then
our sun. I don't understand how that's possible. Bodies of mass act
like points at their center of gravity. If the sun has more than
enough mass to be a black hole then why isn't it one?

If the mass of the sun was somehow squeezed to a tiny radius, would it
become a black hole even though it isn't accelerating and it hasn't
acquired more mass?

For instance, let's say that I control the universe and I decide to
bump up the force of gravity for a bit. I ramp it up so that G is a
quintillion times what it is now. Then, I reduce it back to what it
was. Would the result be that every star in the universe is now a
black hole? Are black holes more a function of density than they are
of mass?

I don't see how that's possible because if that were true, any two
particles that bumped into each other might come together close enough
to become a black hole. I'd think that black holes would be as common
as helium if that were true. (I picked helium because it's the result
of the fusion of two hydrogens which were compressed together by a
star.)

The idea of helium brings up an interesting point. If black holes are
the product of density, how high on the periodic table would we have
to go before an atom of that element was guaranteed to be a black
hole?

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Clarification of Question by mxnmatch-ga on 29 Sep 2006 01:45 PDT

Thanks for the clarification! Good stuff. I'd have responded sooner,
but google never sends me email notifications of activity on my
questions, so I have to come back here on occasion and check my
questions. (Yes, I have it turned on: "E-mail Notifications: Every
time there is activity")

I have a few followup questions:

If black holes are the result of the density of matter, wouldn't that
mean that the big bang theory and black holes are mutually exclusive?
I suppose that isn't really the case since I've always imagined that
the big bang (with inflation) was really just spacetime spurting
through a leak in some other universe (I imagine it ended when the
leak sealed up). But, that last bit was just me making stuff up. I've
never heard of any theories on that topic other than some vague
untestable stuff about a multiverse.

Also, if the density of matter that causes black holes is so high, how
can we possibly know how much gravity is required to cause black holes
to form at the centers of galaxies? Have particle accelerators given
us enough knowledge about the makeup of particles in order to figure
that out? If we've never built a particle accelerator capable of
creating a black hole, how can we know enough about matter at that
level to make predictions about black hole formation?

If the density of mass of a tiny black hole is a deformation in
spacetime then wouldn't that mean that we're still talking about
gravity? I didn't think we knew much about quantum-scale gravity.

It doesn't matter how fast your particle's going, it's not going to
become a black hole.  From the particle's point of view nothing's
changed, though an observer will see it as having gained mass.  This
relativistic mass gain depends on the velocity - it doesn't matter
whether or not the particles's accelerating

>If the mass of the sun was somehow squeezed to a tiny radius, would it
become a black hole even though it isn't accelerating and it hasn't
acquired more mass?

Exactly right - in principle anything can become a black hole if it's
squeezed small enough.  In the case of an atom, that's a lot smaller
than the atom itself, so a couple of them bumping into each other are
way too big to form a black hole.

Ian G.

Hi,

   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.