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JamesAndrix comments on Compartmentalization as a passive phenomenon - Less Wrong
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Hmm, I suppose it's too much handwaving to say it's only a few meters wide and super dense.
My rough calculation says that the density would need to be about a million times greater than Earth's, around 10^10 kg/m^3. This is too low to be a neutron star, but too high to be anything else I think. It may very well be impossible in this universe.
That's assuming uniform density though. Of course you could just have a microblackhole with a hard 1-meter-diameter shell encasing it. How you keep the shell centered is ... trickier.
Similarly, my quick calculation, given an escape velocity high enough to walk and an object 10 meters in diameter, was about 7 * 10^9. That's roughly the density of electron-degenerate matter; I'm pretty sure nothing will hold together at that density without substantial outside pressure, and since we're excluding gravitational compression here I don't think that's likely.
Keeping a shell positioned would be easy; just put an electric charge on both it and the black hole. Spinning the shell fast enough might be awkward from an engineering standpoint, though.
This won't work for spherical shells and uniformly distributed charge for the same reason that a spherical shell has no net gravitational force on anything inside it. You'll need active counterbalancing.
Ah, true, I didn't think of that, or rather didn't think to generalize the gravitational case.
Amusingly, that makes a nice demonstration of the topic of the post, thus bringing us full circle.
Would it be possible to keep the black hole charged (use an electron gun), then manipulate electric fields to keep it centered? I don't know enough physics to tell.
Yes, this could work.