LHC black hole puzzle
 

I don't know if this really counts as a puzzle according to the rules of this forum, but...

Some of the following isn't true, I'm stating it as part of the puzzle. I believe the physics related stuff is true, but I could be wrong. I have added some stuff about the black hole which is obviously not true, but makes the puzzle way more interesting.

It is about 6 months from now, in the future. They have turned on the Large Hadron Collider and are using it successfully. Suddenly, the unthinkable happens, a black hole is created. The event horizon is small(I haven't actually bothered to calculate this), but manages to swallow part of the ring, plus a sphere of earth and air approximately a mile across. Because of some mysterious and unknown aspect of physics(yes, this is kind of stupid) the black hole is created with a momentum exactly equal to the direction of the planet and it's velocity, but not it's rotation. It begins to fall to the middle of the earth, adhering to the known laws of physics, but since it's a black hole there's no terminal velocity for it to reach.

The worlds governments are horrified and leap into action. They call on you to calculate the next few places it will affect so that people can be evacuated and survive for the few years that we as a planet have left.

So, your task is to calculate the first 3 areas it will emerge where it will be directly underneath a land mass so that the people in that area can be evacuated.

mcdonalds, starbucks, walmart

The Whitehouse, The Kremlin, jasong's house.

I just re-read this and realized that the weight of the black hole would make a difference. And then I reconsidered how silly my scenario is.

If you would like to actually calculate the puzzle, then you can either come up with your own weight for the black hole, or simply assume that the weight isn't enough to matter. Of course, if the black hole can successfully swallow a sphere of matter a mile across, it probably weighs a good amount. But since the puzzle was posted in jest, maybe we should simply put it in a Forum like Soap Box.
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Edit: If you like this puzzle idea, I've got another one for you. but we'll wait to see how it goes.

I think it is general good manners to know the answer before you post a puzzle. Otherwise it becomes homework help or just general laziness.

Post a puzzle that has a calculable answer, and actually calculate it yourself to make sure it can be done.

Here are a few considerations:

The average density of earth is over 5 g/cc, but most really dense stuff is well below the surface. Guess: within 1/2 mile of the surface the average density of ground is 2-1/2. Averaged with the negligible density of the half of the sphere that's air, I'd say the initial content of the mile-wide sphere would be, in total, a bit denser than water, say 1.2 g/cc.

Volume of a sphere = (4/3)*pi*r^3.

r = 0.5 mile = 0.8 km

Mass within initial sphere (guess) = 1.2 g/cc * (4/3) * pi * (80000 cm)^3 = 2.6 x 10^15 g

One could expect the BH to pull in (okay, it's really the air pushing into the newly-formed vacuum, gravitational pull not being enough to matter more than a short distance from the BH) a constant flow of air from outside the initial sphere, continuing in down through the tunnel made as it falls. ... But [I]does[/I] the BH make a tunnel as it falls?

I suppose so, since whenever the edge of the event horizon (EH) closest to the center of Earth is close enough to solid ground, it'll pull it into the BH. But the part of the explosive forces generated at that contact point that would project away from the EH might be enough, by opposite reaction, to send the BH up away from the ground! It would be like having a bomb explode at the EH-ground contact point. Hmmm...

So maybe the net result would be that the BH is thrown away from Earth before it sinks down much at all, even though it would swallow about half of that bomb-like explosion within the EH, because the momentum of what it swallowed would be directed away from Earth. If the BH is forced away at escape velocity, then maybe Earth survives after all. But if it isn't, then it just falls back down again after a while and creates a new explosion ... so eventually eats the Earth via a series of EH-ground contact explosions, rather than tunneling.

[QUOTE=cheesehead;162289]Here are a few considerations:[/QUOTE]But, what of the time dialation at the EH? Wouldn't all of this take forever? That again assumes that it doesn't evaporate before it can swallow anything.

[quote=retina;162283]The Whitehouse, The Kremlin, jasong's house.[/quote]

I agree with the last two, but the first suggests you are racist. :furious:

[QUOTE=10metreh;162311][QUOTE=retina;162283]The Whitehouse, The Kremlin, jasong's house.[/QUOTE]I agree with the last two, but the first suggests you are racist. :furious:[/QUOTE]Don't blame me, blame the people that named it!

[size=1]I'm not racist, I hate everyone.[/size]

[QUOTE=Uncwilly;162298]But, what of the time dialation at the EH? Wouldn't all of this take forever? That again assumes that it doesn't evaporate before it can swallow anything.[/QUOTE]No. Time dilation is a myth promulgated by observers at infinity. The proper time for material to reach the singularity is finite, and very small for a BH of such tiny mass.

The temperature, in geometric units, of an uncharged non-rotating BH of mass m is 1/(4\pi m).

Plugging in m=10^15 g gives a temperature of around 10^11K. Pretty hot and the peak radiation is way out in the hard gamma rays, but it isn't going to evaporate any time soon (I make the lifetime around 10^10 years), especially as it is about the size of a proton (10^-15m) and so is radiating from a very tiny area. The collision cross section for sucking in terrestial matter will be correspondingly small and the gamma radiation pressure will tend to keep stuff away from the hole.

Sorry to dampen the melodrama bu,t while this thing would be nasty source of hard radiation in its immediate vicinity, it's not an earth-swallower on human time scales.

Paul

[QUOTE=xilman;162327]Plugging in m=10^15 g gives a temperature of around 10^11K. Pretty hot and the peak radiation is way out in the hard gamma rays, but it isn't going to evaporate any time soon (I make the lifetime around 10^10 years), especially as it is about the size of a proton (10^-15m) and so is radiating from a very tiny area. The collision cross section for sucking in terrestial matter will be correspondingly small and the gamma radiation pressure will tend to keep stuff away from the hole.[/QUOTE]
My understanding is that any BH that the LHC could create would weigh in closer to 10^[COLOR="Red"][B][SIZE="4"]-[/SIZE][/B][/COLOR]15 g. Even allowing for substantial mass gain from the input energy , the total mass should be on the order of 10,000 amu.