If it's in a stable orbit in the solar system, it wouldn't be able to "eat" us. Black holes gravitate exactly the same as any other mass, so it would have the same gravitational effect on Earth as any object if the same mass.
What makes black holes special is that you can get much close to their center of mass than you can with normal objects. When you're that close - inside the radius that a normal density object of that mass would have - then you experience gravity at a much higher strength than normal.
Put another way, even if our Moon was a black hole with the same mass, very little would change except that it would no longer reflect sunlight. Ocean tides on Earth would remain the same. You wouldn't want to try to land on it though...
There was a movie where Moon was a hi-tech 'megastructure' with a white dwarf inside. I wonder if it would be theoretically possible to set up such a mini-dyson sphere around a mini-blackhole.
A black hole, or neutron star, would make much more sense in that scenario than a white dwarf.
A white dwarf smaller than the moon seems unlikely, if not impossible. If it were that small, unless it was in the (fast) process of collapsing to a neutron star, it wouldn't have enough mass to remain that compact.
A neutron star or black hole would work fine, because both can easily have radii much smaller than the Moon's.
> “There are just so many things wrong with [the idea of a white dwarf inside the moon],” says Romer. “Now, a white dwarf is a very compact object. But, you know — people have heard of neutron stars — neutron stars are ultra-compact objects, they’re a few tens of kilometres across. White dwarfs are actually about the size of a normal star.”
You can come up with scenarios where white dwarfs are much smaller than a star, but smaller than the Moon is iffy at best.
As for the Dyson sphere idea, the biggest problem with it in this scaled-down scenario is stability. You can't exactly support it with struts, or something.
On that subject, I highly recommend the video "dyson spheres are a joke": https://www.youtube.com/watch?v=fLzEX1TPBFM , by astrophysicist Angela Collier. But you need to either watch all 53 minutes, or skip to near the end, to find out just how literal the title is.
If you set it up at the right radius it would have 1g gravity at the surface, like a little mini-world. It wouldn't be able to hold an atmosphere though, so it would have to have pressurized buildings on it.
What makes black holes special is that you can get much close to their center of mass than you can with normal objects. When you're that close - inside the radius that a normal density object of that mass would have - then you experience gravity at a much higher strength than normal.
Put another way, even if our Moon was a black hole with the same mass, very little would change except that it would no longer reflect sunlight. Ocean tides on Earth would remain the same. You wouldn't want to try to land on it though...