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I was just rambling, as well. I do that sometimes.I'm not an expert on black holes, but it seems to me that they needn't be small, at least not when they're first formed. Also, they don't even need to be dense at first, if there's enough matter. The escape velocity is determined by equating kinetic energy to gravitational energy and solving for velocity:
½mv² = GMm/r
½v² = GM/r
v = sqr(2GM/r)
Then assume the escape velocity is the speed of light:
v = c = sqr(2GM/r)
We can then find the Schwarzschild radius by solving for r:
r = 2GM/c²
Next assume that we have a giant, homogeneous sphere of density p. We can define it as:
p = M/V
where the volume V is defined as:
V = (4/3)*pi*r³
If we choose a value for p, we can then solve for the radius at which it forms an event horizon. This would be a sphere that just barely forms a black hole.
p = M / ((4/3)*pi*r³)
M = ½rc²/G
p = ½rc² / ((4/3)*G*pi*r³)
p = (3/8)c² / (G*pi*r²)
r² = (3/8)c² / (p*G*pi)
r = sqr((3/8)c² / (p*G*pi))
It comes out to a huge number, but it's not infinite for any nonzero density. It makes me wonder how much interstellar hydrogen, etc, is required for a black hole to spontaneously form.
*shrug* I'm bored. lol
All this math makes me realize what CERN could be doing -- creating artificial black holes via math. In other words, perhaps with math and physics we can create a singularity that doesn't suck us all into oblivion. But I really have no idea if that is possible or how to do it.
BTW, a sphere doesn't need to be giant to be dense, but you've already shown that above M/V -- mass doesn't indicate size.
Just thinking out loud again.
At CERN, they'd most likely use relativistic mass increase which happens near light speed in order to create a black hole. The equation is:
m = m0 / sqr(1 - (v/c)²)
where m is the relativistic mass, m0 is the rest mass (which is constant), v is the velocity of the particle, and c is the speed of light.
The shape and size of the particle also change, but it should be possible to calculate the velocity at which it has the right mass and volume to form a black hole (I'd have to look up the other equations). This is because the mass approaches infinity as the particle velocity approaches the speed of light.
The problem they'd face after formation of a tiny black hole would be containment, and the likely solution would be to collide it with another black hole of equal mass.
This is all speculation though.
In other words, Titor's concept of a microsingularity isn't impossible.