Why useful? Considering how hard of a time astronomers are having to simply find it it’s hard to imagine it being easy to study.

A black hole in our solar system is basically "in our backyard" in relation to typical interstellar distances.

Sure, we wouldn't be able to get there for many decades, but "within a century" would be feasible.

There are so many unknowns surrounding the nature of black holes. Having one in our backyard would give us a chance to test our guesses.

A black hole reachable in a human lifetime with ordinary chemical rockets would be an amazing laboratory for extreme physics.

What's the first thing we throw in?

>What's the first thing...

Naah, boring. Who's the first person we throw in?

Yeah, finding it is hard, but once you've found it, sending a probe would be totally doable. I think it would be worth it.

Aside from research, it could be used to provoke time dilation, though I’m not sure how much you could get out of a basketball sized black hole.:8

If you're interested in creating time dilation, then a planetary mass black hole unfortunately won't get you any further than, well, a regular planet with the same mass.

(Aside: time dilation already occurs on and around Earth. GPS satellites have to account for the fact that time runs ever so slightly slower on the ground.)

So, it’s not the local strength of the gravitational field, but the overall mass that matters? How does that work? I mean, if distance/ intensity doesn’t matter, than distance is irrelevant? That seems extremely counterintuitive.

I thought that since you could get into areas where the field was arbitrarily intense, that it would be able to provoke significant relativistic effects.

I had assumed that the small mass would make tidal forces more problematic than with a larger one, but if the distance/intensity of the field isn’t a factor, but only the overall mass… wouldn’t that mean that we could utilize black holes at arbitrarily long distance to provoke those effects, so it would just be a universal constant based on the mass of the universe, and there would be no relativistic effects on a relative basis?

What am I missing here?

I don't think that's right except at a radius of a typical planet. At the event horizon of even a planetary mass black hole, gravity is so strong that light cant escape, and the time dilation effect should be the same as for any event horizon.

Not really, the max acceleration/gravity you can get from earth is around 1G. Even if you tunneled to the center of the earth, you'd get ... zero g.

However with an earth max black hole you could get closer, which would have a higher acceleration, and would time dilate more strongly.

Not only would it be insanely cool, it'd give us a once-in-a-lifetime chance to study something that might've formed in the first moments of the universe

I mean, if it's there, we can study it as many times as we want in our lifetime.