Q: How bad would it be if we accidentally made a black hole?

Physicist: Not too bad!  Any black hole that humanity might ever create is very unlikely to harm anyone who doesn’t try to eat it.

Black holes do two things that make them (potentially) dangerous: they eat and they pop.  For the black holes we might reasonably create on Earth, neither of these is a problem.

Home-grown black holes: not a serious concern.

The recipe for black holes is literally the simplest recipe possible; it’s “get a bunch of stuff and put it somewhere”.  In practice, you need at least 3.8 Sun’s worth of stuff and the somewhere is anywhere smaller than a few dozen km across.  That last bit is important: the defining characteristic of black holes isn’t their mass, it’s their density.

For a given amount of mass the same amount of gravity “flows” through every containing surface.  In this picture, the same total gravity points through both outer surfaces if they contain the same total mass.  But if all of the mass is concentrated in a tiny place (as it is on the right), then the gravity through the smaller surface must be stronger in order to equal the weaker gravity through the larger surface.  Fun fact: this can be used to derive the inverse square law of gravitation and/or is a consequence of it.

If you’re any given distance away from a conglomeration of matter, it doesn’t make much difference how that matter is arranged.  For example, if the Sun were to collapse into a black hole (it won’t), all of the planets would continue to orbit around it in exactly the same way (just colder).  The gravitational pull doesn’t start getting “black-hole-ish” until you’re well beyond where the surface of the Sun used to be.  Conversely, if the Sun were to swell up and become huge (it probably will), then all of the planets will continue to orbit it in exactly the same way (just hotter).

To create a new black hole here on Earth, we’d probably use a particle accelerator to slam particles together and (fingers crossed) get the density of energy and matter in one extremely small region high enough to collapse.  This is wildly unreasonable.  But even if we managed to pull it off, the resulting black hole wouldn’t suddenly start pulling things in any more than the original matter and energy did.

For comparison, if you were to collapse Mt. Everest into a black hole it would be no more than a few atoms across.  It’s gravity would be as strong as the gravity on Earth’s surface within around 10 meters.  If you stood right next to it you’d be in trouble, but you wouldn’t fall in if you gave it a wide berth.  In fact, that’s why mountain climbers aren’t particularly bothered by Everest’s mass; even if you’re literally standing on it, you can’t get within more than a few km of most of its mass (fundamentally, Mt. Everest is a big, spread out, pile of stuff).

But the amount of material used in particle accelerators (or any laboratory for that matter) is substantially less than the mass of Everest.  They’re “particle accelerators” after all, not “really-big-piles-of-stuff accelerators”.  The proton beams at the LHC have a mass of about 0.5 nanograms and when moving at full speed have a “relativistic mass” of about 4 micrograms (because they carry about 7500 times as much kinetic energy as mass).  4 micrograms doesn’t have a scary amount of gravity, and if you turn that into a black hole, it still doesn’t.  A black hole that small probably wouldn’t even be able to eat individual atoms.  “Probably” because we’ve never seen a black hole anywhere near that small.

The other thing that black holes do is “pop”.  Black holes emit Hawking radiation.  We haven’t measured it directly, but there a some good theoretical reasons to think that it’s a thing.  Paradoxically, the smaller a black hole is, the more it radiates.  “Natural” black holes in space (that are as massive as stars) radiate so little that they’re completely undetectable (hence the name: black hole).  The itty-bitty black holes we might create would radiate so fast that they’d be exploding (explosion = energy released fast).  The absolute worst case scenario at CERN (where all of the 115 billion protons in each of the at-most 2,808 groups moving at full speed are all piled up in the same tiny black hole) would be a “pop” with the energy of a few hundred sticks of dynamite.

That’s a good sized boom, but not world ending.  More to the point; this is exactly the same amount of energy that was put into the beams in the first place.  This boom isn’t the worst case scenario for black holes, it’s the worst case scenario for the LHC in general (cave-ins and eldritch horrors notwithstanding).  It is this “pop” that would make a tiny black hole a hazard.  The gravitational pull of a few micrograms of matter, regardless of how it is arranged, is never dangerous; you wouldn’t get pulled inside out if you ate it.  However, you wouldn’t get the chance, since any black hole that we could reasonably create would already be mid-explosion.

A black hole with a mass of a few million tons would blaze with Hawking radiation so brightly that you wouldn’t want it on the ground or even in low orbit.  It would be “stable” in that it wouldn’t just explode and disappear.  This is one method that science fiction authors use for powering their amazing fictional scientific devices.

The kind of black holes that we might imagine, that are cold (colder than the Sun at least), stable, and happily absorbing material, have a mass comparable to a continent at minimum.  Even then, it would be no more than a couple millimeters across.  These wouldn’t be popping or burning things with Hawking radiation.  The real danger of a black hole of this size isn’t the black hole itself, so much as the process of creating them (listen, I’m making a black hole, so I need to crush all of Australia into a singularity real quick).

We have no way, even in theory, to compress a mountain of material into a volume the size of a virus.  Nature compresses matter into black holes by parking a star on it.  That seems to be far and away the best option, so if we want to create black holes the “easiest” way may be to collect some stars and throw them in a pile.  But by the time you’re running around grabbing stars, you may as well just find an unclaimed black hole in space and take credit for it.