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Of course if we had a black hole in a lab (or one in a convenient orbit) we could run all sort of experiments, but which experiments exactly? We will start by throwing things at it and watch, obviously, but that's unimaginative. What are the smart experiments?
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If you had a small black hole in a lab you could generate power from the hawking radiation, likely enough to power the entire world. A 1,000,000 ton black hole would last over a thousand years without feeding it more mass and produce about 300 TW of energy (increasing over time, so you better keep feeding it). You'd also need some pretty good sunglasses to be able to watch things being thrown into it. Also I'm not sure how you could throw anything into it given the amount of radiation pressure... Maybe a dedicated particle accelerator could do it.

Anything smaller while also lasting long enough to do an experiment on and you'd likely end up producing too much energy and destroying the planet.

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So the hawking radiation is so strong that it impedes matter falling into the hole?

And can you charge the hole with enough of a charge to use electromagnetism to move and contain it?

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Yes the event horizon would be smaller than the width of a proton. Good luck getting anything into that with 300 TW of gamma rays coming out of it.
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> which experiments exactly?

Put a bunch of charge into it to generate a naked singularity. Then look at it.

More usefully: perfect the Penrose process.

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There's a few obvious things. What you've got is an almost "vertical" gravity well near the object. A smaller black hole would actually have a steeper gravity well than a large one.

(1) See how gravity behaves at those strengths and scales by firing lasers and particle beams past it, grazing the event horizon, and use that information to test quantum gravity hypotheses and things like string theory. Classical gravity predicts certain results. Quantum and non-classical theories would make different predictions. For example, you might see direct evidence of gravitational quantization very close to the horizon.

(2) Chuck stuff into it: heavy ions, small masses with a coilgun. Measure the results: spectrum, particles emitted, etc.

(3) Chuck stuff into it in a very precise way and use its extreme near-horizon gravitational well as a particle accelerator to achieve collision energies potentially millions of times greater than the LHC. You would not be able to directly observe these collisions, but you could potentially observe stuff kicked out. Orbit it with an array of sensors and magnetic traps.

Bonus: use its gravity well to yeet small probes at interstellar velocities (a few percent 'c' or higher) for flyby missions to photograph exoplanets? I believe you could use the Oberth effect here and do something like fly very close and fire a single Orion-style nuclear pulse at a sacrificial pusher plate. The impulse would accelerate the payload to insane velocities.

No human passengers though, since the acceleration would probably do this: https://www.youtube.com/watch?v=waG8YYTwpAQ

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I'm not sure anything after the event horizon right? Since no light == no information.
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Can magnetic fields escape, if their lines intersect the event horizon of a black hole?
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We could probably redirect budget for next gen particle accelerator to building an experimental platform orbiting the black hole, and get better results, right?
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I’m still convinced a muon collider is the best bang for the buck for a next-generation collider. It requires new engineering and could probe new physics.
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What could go wrong?
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Not much.

A black hole isn't a magic cosmic vacuum cleaner. It's a dense piece of mass. An asteroid mass black hole the size of a hydrogen atom would be... an object the size of a hydrogen atom with the mass of an asteroid. You could orbit it and the orbital calculations, at a reasonable distance, would be the same as orbiting an asteroid. You just can't get too close or you get into that steep gravity well and "become physics" (spaghettification etc.).

It would have an insanely steep gravity well, but you'd have to get close to actually feel it. It would rarely interact with mass naturally. We could chuck stuff into it or fire lasers and particle beams at it to study it, of course, but to hit it we'd have to fire it at the right angle and velocity to negate the orbit and fall into it. Orbital mechanics still works the same way.

If a black hole this size flew through the Earth at high velocity, it might not even do anything. It'd be like a bullet being fired through a puff of smoke. It might leave some kind of trail if you knew exactly what to look for and where to look, something almost analogous to the trails left by particles in a chamber.

I've given this example multiple times because it illustrates the point well, I think.

If you could magically transform the Moon into a black hole of the same mass, you would now have an object of that mass about the size of a BB or a small marble orbiting the Earth right where the Moon's center of mass orbited. The tides would continue as normal, since its gravitational effects on the Earth would be the same at that distance. Probes and other objects orbiting the Moon would continue to orbit it.

You just wouldn't be able to see it anymore. If you focused a very good telescope on its location, though, you could probably see gravitational lensing of the star field behind it.

The only risk might be if a large object actually hit it, in which case the accretion disc might temporarily emit enough X-rays and gamma rays to be harmful to Earth. Not sure though. It might not be that harmful at that distance.

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As is often the case (and I suspect you're already familiar with it) Randall Munroe tackled the moon->black hole question:

https://what-if.xkcd.com/129/

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How certain is the evaporation? Obviously Hawking radiation has never been observed, but is it tied in enough to other known physics that we can be reasonably certain it exists?
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It's a very strong consensus among physicists, but has not been observed. My understanding is it pops right out of the math. If it doesn't exist it means some new fundamental physics is in play, like quantum gravitational effects we don't understand at all right now.

If it doesn't exist its also has profound implications for the long term fate of the universe, since it would mean black holes never evaporate.

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My pet theory is that supermassive black holes are older than the universe and they didn't grew much.
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Does PBH theory also predict >1 billion solar mass black holes so early?
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I believe it does, due to PBHs forming seeds for early accretion, but ask a non-armchair physicist (or a good LLM).
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