Black holes can't evaporate now because the cosmic background radiation is too hot. The black holes are colder the CMBR, so they absorb heat and grow (albeit very, very slightly).
Eventually the CMBR will cool down and the holes will be able to evaporate, but not for an insanely long time.
I believe that LHC has no chance ever to harvest enough energy to create a sensible-sized black hole. It’s still mc-squared (give or take an order of magnitude and my layman mistakes), so 1g BH takes about 1e14 joules or 5 minutes of average EU electricity output. Also, there is no sea nearby to cool it off afterwards. Also, a planck-sized BH weighs 1e-5 g.
A mass similar to Mount Everest[13][note 1] has a Schwarzschild radius much smaller than a nanometre.[note 2] Its average density at that size would be so high that no known mechanism could form such extremely compact objects
It seems that at energies available to us they are basically either virtual or non-existent. This contradicts the common notion that cosmic rays create microbhs occasionally, but I guess we have to wait for a physicist to clarify this.
In theory, it might have made a black hole. It would have lasted a ridiculously small period of time, but be quite recognizable by the energy it gave off. Instead of the usual decay patterns, it would give off a spray just of photons, like a black body at a recognizable (and very high) temperature.
We didn't see that, and in fact theory predicted that it was insanely unlikely that we would. But there's nothing wrong with the possibility of a black hole much, much, much smaller than a gram, with a radius smaller than the Planck length.
If we had seen it, it would have been insanely informative. But it wasn't ever gonna happen.
The difficulty in producing a black hole is getting the energy density high enough. We have no known mechanism to get an energy density that's even close the right order of magnitude.
Maybe you meant that in theory quantum fluctuations might do it? Unfortunately, this is really a non-answer. The probability is so ridiculously low that it's not practicably distinguishable from zero. (It's _vastly_ more likely that every measurement ever taken and that _will_ be ever taken is wrong, than that the event actually happened).
I have to use "theory" loosely here, because there isn't any known or suspected way to do it. The energy, as you observer, is off by orders of magnitude.
It's just that it's "merely" orders of magnitude. The odds were ludicrously low, but with a whole lot of particles being collided. So maybe, ridiculous outside chance, they might see one event out of the 10^20 events to be observed.
But almost certainly not. So it was never worth talking about. But people loved to talk about black holes, so the math got done.
Correct. It's not so much that the small ones are unstable, but just that there's a continuous curve of lifetimes that's a function of mass.
For the LHC, the lifetime of a black hole it could conceivably create would be 10^-86 seconds. It didn't even do that, but if it had, it would have evaporated before it moved the diameter of an electron. There's no functional difference between that black hole and a vastly bigger one besides the mass... but it's a difference of many, many, many orders of magnitude.
I'm not trying to nitpick, just trying to get my head around your original claim, which I'm tempted to amend:
> Black holes [above a certain mass] can't evaporate now because the cosmic background radiation is too hot
And that mass--the Stable-Black-Hole-In-A-Vacuum mass--it's decreasing. And whatever it is at a given time, more massive holes grow, and less massive holes shrink. Do I have that right?
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I'm trying to extrapolate backwards to a time when the universe was hotter and the SBHIAV mass was smaller. It seems like there ought to have been a point when the universe was so hot that holes expanded greedily, perhaps to the point where the expanding universe couldn't escape. Golly I wish they taught cosmology at my local university...
Eventually the CMBR will cool down and the holes will be able to evaporate, but not for an insanely long time.