So at what mass does a black hole become sustainable? IOW, when does Hawking radiation of mass/energy away from it become less than mass/energy pouring into it? I can't imagine the LHC being able to create that level of output.
Assuming Hawking radiation is true, there is no "sustainable" black black hole mass, at least in absolute terms. But you're correct. the LHC might be able to produce momentary sub-atomic mass black holes. The entire energy output of Human civilization for several years wouldn't be enough to make a big multi-ton hole. And the collider machinery would probably have to be orbital in scale. Anything built on Earth might not be big or long enough.
All of them "evaporate" through Hawking radiation. However the larger and more massive they are, the slower they evaporate. Stellar sized holes on up would last billions, maybe trillions, quadrillions of years past the cold black "heat death" of the Universe, assuming the it's expanding forever.
What you really mean is "how large" (massive) must a black hole be for it to last a meaningful duration on a human timescale and start making us worry if we uh... "dropped it"? Probably at least a few tons in mass. But it would be hellishly radioactive, the virtual particles of Hawking radiation becoming "real" are expressed as intense gamma radiation.
Even if you could make a multi-ton black hole in an Earth-bound lab, the horrendous gamma radiation from the Hawking radiation might be vaporizing matter surrounding it into plasma. Could reduce the efficiency with which it can eat more mass if all the black hole was grabbing was hot plasma and not solid matter. Even a multi-ton black hole would have an event horizon that's a single atom in size.
I'm not any kind of physicist, and I haven't a clue if it would eat faster than it could radiate even if it fell into the Earth.
The problem with such a "large" multi-ton quantum singularity is that it's a nasty catch-22. If a micro black hole "starves" the Hawking radiation reaches exponential growth as the black hole loses mass in a feedback loop, because the smaller the event horizon, the more efficiently it radiates away it's mass as Hawking radiation. It ends as a gamma ray "burster" which would probably destroy the Earth, or at least leave much of it mostly molten.
If you keep "feeding" it, it gets bigger, that's not good if it's on the Earth either.
Just curious, but how many people might it take to constitute sufficient genetic diversity?
There's no set number.
It matters more what the acceptable rate of incest, genetic defects, and stillbirths, and birth defects is to your group. And what level of medical technology and scientific knowledge the group is able to maintain.
If you start with a group that was both diverse, and screened genetically as well as possible, and they have access to a qualified geneticist each generation, and everyone's okay with each woman bearing multiple children from different men... And maybe you use IVF technology and perform embryo screening etc. You could probably make it on 200-500 people. Although after just a few generations, the group might start to look "a little funny" and might not even out to something like an Earth-like spread for thousands of years.
IIRC, the human matrilineal mitochondrial DNA record suggests that humanity, or our precursors were winnowed down to just a handful of fertile women at more than once in the stone age and pre-stone age. So it's do-able with less, but the infant mortality rate and exiled individuals left to die etc. must have been horrendous. And it may not have been possible at any time before the invention of agriculture, where the winnowing effect on humanity began to ease.
I think the number to "make it" with no extreme measures, allowing people to pair up into traditional families is somewhere north of 2000 people. Maybe 3500 to be safe. The Amish are often studied to see what happens in that kind of situation. They have limited access to outbreeding, and it's made worse by the fact people leave the fold, but rarely, if ever, do outsiders convert and join their ranks.
They have a higher incidence of certain genetic diseases and birth defects than the population at large, but it's not enough to do them in.
