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But it wouldn’t sit there, would it? Wouldn’t it suck itself down into the Earth and suck the Earth into it? I realize you’re just painting a picture here, but it raised the question in my mind. Is it possible to contain a black hole?
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Well, yeah, we’ve been kind of assuming it’s being held in place somehow. If it falls into the Earth’s core, whether it will eventually suck the whole Earth into it depends on how quickly it eats matter, relative to how fast it emits Hawking radiation. My gut feel is it’s large enough that it would grow. One that only weighed a gram or so would evaporate. Not sure what mass would be at the tipping point between growing and shrinking.
Yes. The textbook method is to give it an electrical charge, and then put it in a whopping big electric field.
Exponential. Or rather, a combination of exponential and inverse square called the Yukawa field, but the exponential part is what’s really important. Strictly speaking, no known force actually exactly follows the Yukawa law, but it’s a reasonable approximation.
My gut feel is that it’d actually evaporate before it even reached the floor, well before we got into the question of cross-sections and sectional density of the Earth.
The 652 million ton black hole? This site says 700 billion years.
What do you mean by “it”?
I’m talking about a real block of real granite. Said block of granite would just sit there exactly like every other big hill or baby mountain-sized hunk of rock that naturally occurs on Earth. And no, it would not have any more tendency to collapse into a black hole than does the Ayers Rock in Australia or Half Dome in Yosemite, etc. It’s just a big (on human scale) lump-o-static-rock. Yes, if it was sitting on soft sandy soil it’d tend to sink in. But that’s just macro scale buoyancy at work and months or years would pass while it slowly settles some distance into softer soil.
Conversely, if by “it”, you mean a 652MT proton-sized black hole …
Well that wasn’t what I was talking about.
If a proton-scale BH was magically released at eye level near you I suspect it will accelerate towards the ground at 9.8 ms[sup]-3[/sup] like anything else does then would slide neatly between the atoms of the dirt it landed on. And continue slipping between atoms, occasionally absorbing one the BH happened to hit head-on until the BH settled at the center of the Earth.
At which point nothing much would happen. Every so often (days, years, I have no clue) the BH would absorb another atom. The Earth has enough atoms to give them up at that rate for a very long time.
Yes, over time the BH would grow from the Earth atoms it’s absorbing. But IMO the Sun will engulf the Earth long before the protonic BH does.
The formulas for luminosity and hence lifespan are actually much more complicated than what’s on that site, since it depends on the mass and spin of all of the particles which could potentially be emitted by a black hole (which is, eventually, all of them, once it gets hot enough). But the rough scaling they show is still correct, which means their figures should be right to within an order of magnitude or so. So, my intuition on this point was wrong.