However, that 4 billion g acceleration is a problem even if it is only for a very short time. If the black hole is going at .999999999c, which is far more than we can hope for, something withing about 100m it's path would be accelerated due to the gravity of the black hole so much that it ends up moving at hundreds of thousands of miles per hour, and stuff within a few dozen meters becomes relativistic. Even ignoring the stuff very close to the path of the black hole, the stuff at hundreds of meters from the path would release an epic amount of kinetic energy. My envelope isn't large enough to see just how large, but certainly enough to leave a melted/vaporized tube at least a few hundred meters across all the way through the earth, and this is a gross underestimate.
Yeah, but you're not accounting for all the kinetic energy the black hole is going to impart on the Earth, which is the main factor in this hypothetical disaster.
Let's assume for simplicity that the radius of the Earth is 5000 km, and the black hole is moving at 1000 km/s.
That means that as soon as it's approximately 5000 km out we'll have around 5 seconds where around half of the Earth isn't the Earth's surface in any meaningful sense anymore, rather it's a bunch of rocks that have just crossed the zero G barrier between the Earth and the black hole, and are now in freefall "upwards" from the Earth.
I'm too lazy now to calculate how far a rock on the surface will travel "upwards" given the approaching black hole, but let's just assume a constant 9.8 m/s^2 for the whole 5 seconds to understate this disaster (it's going to be a lot more than that). You'll fall ~120 meters in 5 seconds in freefall in Earth gravity.
So by the time the black hole passes the "crust" that crust is already hovering some hundreds of meters in the air, and will rapidly fall down and re-compress as the black hole passes.
I wouldn't be surprised if the energy transfer is enough to turn the entire surface into liquid magma, but I haven't done that back-of-the-envelope calculation.
You are assuming the stuff near the surface is being pulled up, but the stuff under that isn't being pulled up, so rocks are 'flying away from the earth and towards the black hole'. In reality the only net force you can 'feel' from gravity is due to tidal forces, so this would have an effect more like 'squeezing' the earth and the energy would be spread throughout the entire interior. For an earth-mass black hole, however, the difference in acceleration between something 1000km away and something 2000km away is still stupidly high (about 30g), so your assumption is correct!
But generally, this is my point. A slow moving black hole is going to rip the earth apart, a fast moving black hole is 'less dangerous' because it just punches a hole and keeps going, with almost no interaction with the earth, even though that is counter-intuitive. Yes, things would get pulled away from the surface of the earth, but they would only feel that pull upward for a very, very short amount of time, not long enough to be substantial. A small black hole, say the mass of a meteor or something, might go through the earth and not even be noticed, it's far less dangerous than a meteor of the same mass would have been.
A fast moving black hole isn't 'nearby' very long, it would go from far away to far away in microseconds.
However, as the mass gets large enough, the dynamical friction on the black hole is so large that it leaves behind significant kinetic energy by melting a hole through the earth, no matter how fast it is going. https://en.wikipedia.org/wiki/Dynamical_friction
If you neglect dynamical friction, as far as I know an earth mass black hole could potentially go right through the earth and we wouldn't have to worry so much, but it depends on the specific path it takes since it could still disrupt the Earth's orbit.
Would make for a pretty impressive anti-podal volcano if nothing else.
I did hear one theory that the Tunguska event was an evaporating black hole, I don't think there's much scientific evidence to back that up though.
I forget the story, but some scary advanced weapon technology gets abandoned, sold on the black market, and ends up in India. Random folks there figured out you could chip the containment vessel, feed it sewage, and bounce a laser off it to capture energy and power the village. Complications ensue.
