# Would a mini-blackhole collision with Earth cause heating? [duplicate]

Let's forget about the probability of this event. I am a mad scientist on the Moon, I created a micro black hole of the diameter $r=0.5cm$. I have to be fast before it evaporates due to Hawking radiation, but before shooting it to the Earth, doubt stops me.

As soon as my blackhole reaches the ground (and even before), it starts sucking material. Everything it "touches" would disappear under the event horizon. It couldn't create shockwaves and alike. How could then it produce the massive blast of heat and destruction it supposed to?
I consider two scenarios:

1. The black hole travels to the Earth with relatively low speed. This way the (zero) momentum of the material it sucks during interaction would slow it down enough to finally stop. After that, it would slowly but surely consume the whole Earth. This is the less interesting problem therefore.

2. The black hole hits Earth with a significant portion of light speed. It wouldn't even bother with the sucked material, even the whole planet couldn't stop it. Speaking of an asteroid, this would be the holly way of total destruction. But I have an event horizon...

So, there is the question:

In both cases, would it, and if, by what effect and how much would the black hole heat up the impact zone?

I have some theories. Maybe the gravitational turbulence the encounter causes locally would cause enough heat to be destructive. This seems to work only for the first case: a speeding hole would have little time to accelerate the ground material. Maybe the material it sucks up would emit strong enough radiation. Or the collision's energy would indeed only increase the black hole's mass, and I would only get a neat 0.5cm wide hole in the ground with slowly (?) rising diameter. (In this case, I'd wonder if any friction-like phenomena would occur apart from the momentum of sucked material...)

Note: I am not interested in the effects of Hawking radiation of the black hole, though I don't know how significant would it be. If it is so big it makes the neglection unrealistic, feel free to produce a bigger mini-blackhole.

• Unless I'm doing this wrong, putting in a 0.5 cm radius gives a mass of $3.4\times10^{24}\,\mathrm{kg}$ which is a bit bigger than 37 kt. – Kyle Kanos Jan 16 '17 at 19:39
• @KyleKanos oops, you are right. I forgot that the expression I used choosed c=1... I remove the comment on the mass. – Neinstein Jan 16 '17 at 19:44
• Related: physics.stackexchange.com/q/2743/2451 and links therein. – Qmechanic Jan 16 '17 at 19:44
• Probably also related: physics.stackexchange.com/q/172403 – Kyle Kanos Jan 16 '17 at 19:51
• @KyleKanos I indeed didn't find it before, but that question (and the answers) seem to focus on the global impact including the Earth's movement, while I focus on local effects near the impact zone, especially heating. – Neinstein Jan 16 '17 at 19:54

## 1 Answer

A black hole with radius $r~=~.5cm$ $=~2GM/c^2$ leads to the mass $$M~=~\frac{rc^2}{2G}~=~3.38\times 10^{24}kg.$$ This is nearly the mass of the Earth. This is not a microblack hole, but a sort of midi-mini-black hole. If the moon were a black hole it would have a Hawking radiation temperature equal to the CMB background. This black hole would be colder. So Hawking radiation would not be a problem with respect to this black hole. However, the gravitation of the black hole would be significant and the collision would be a bit like a bullet smashing a watermelon to bits.