On the immediate effects of a small, short term black hole

Question

What immediate effects would a small, short-term black hole have if it appeared in a residential backyard? How small or short-lived would it have to be to be survivable, if it is survivable at all?

In said backyard, there are four children, a garden, a tree house, and lots and lots of monsters.

Answer 1

Black holes are actually more like gravitational point-sources than anything. Unlike their depictions in movies, black holes emit only as much gravity as the object that they are made from. For example, if the sun were to suddenly turn into a black hole, the earth would keep orbiting it just like it normally would.

That aside, the two major dangers of black holes are tidal forces near the event horizon, and the event horizon itself.

First the event horizon: the formula for the radius of the event horizon is

$r=\frac{2Gm}{c^{2}}$

According to this formula, a black hole with the same mass as the earth would have an event horizon less than a millimeter in radius. A black hole with a similar mass to a human would be smaller than a single proton. Obviously this isn't much of an issue.

However, the tidal forces are. Tidal forces occur when the gravity at one end of an object is different than the gravity at the other end, stretching the object. The tidal force exerted by the black hole would be:

$F=\frac{μlm}{4r^{3}}$

Assuming the black hole is 1 meter away from a 1 meter tall human who weighs 60 kilograms, you get:

$F=15μ$

Most humans can survive about 8gs, which in the case of our hypothetical human would be about 588 newtons. Substituting that into the equation, you get:

$588=15μ$

$39.2=μ$

Since μ, the standard gravity, is equal to:

$μ=GM$

The maximum survivable black hole would be several trillion kilograms massive. However, the earth would take vastly more damage in this scenario. Any black hole that would locally exert force on the order of magnitude that the earth exerts would begin to suck parts of the earth into it.

So to summarize, it would either be incredibly boring, or everyone would die.

Answer 2

I recommend the Hawking radiation calculator linked by Philipp: http://xaonon.dyndns.org/hawking/

The general point is that black holes convert themselves to energy: the lifetime of a black hole is proportional to the cube of its mass, and in that time all its mass will be converted to energy per Einstein's formula $E = mc^2$

You can use this and a few handy approximations (such as: 1 kg mass conversion to radiation is 21.5 megatons TNT equivalent) to divide black holes into a few mass ranges:

• Up to one microgram: it's anyone's guess whether these can actually exist, since their lifetime is less than the Planck time. At 1 microgram they release 21.5 tons TNT equivalent. So, you never see the black hole. Rather, there's a sudden large explosion. If you're in the back yard with it, you die, and you never know what hit you.

• 2kg: lifetime is still negligible (less than $10^{-16}$ seconds), so it explodes immediately. It's at 43 megatons, close to the largest nuke ever detonated. Nobody in the town survives. The range from 1 $\mu g$ to 2kg can be thought of as an increasingly large explosion on the scale of explosions caused by humans. It doesn't have exactly the same energy profile as a nuke, but there's no "safe" way to release that much energy.

• 100 tons: black hole lasts for 0.1s, which is long enough for it to fall 5cm straight down. So in that sense, it does something before it's gone. Anyone standing anywhere near it would of course be instantly vaporised by its radiation, so wouldn't be able to watch that happen.

• 500 tons: black hole lasts 10s, which at least in theory is long enough to absorb significant mass to counter-act evaporation. In practice, it's much smaller than a proton, and it's still radiating so fiercely ($10^{12}$ gigawatts) that everything near it is driven away. So it won't actually encounter much matter. Most of its energy is released underground, but it only has time to fall 500m, so it's still in the crust. A huge chunk of crust above it is blasted into the atmosphere, in an event considerably worse than Krakatoa.

• 4500 tons: lifetime is now over an hour, plenty of time to fall through the earth, perhaps reach the surface on the opposite side or close to it, then fall through the centre. Size still much smaller than a proton. Energy released is approximately that of the impact that created the Chicxulub crater 65 million years ago, and caused the extinction of the vast majority of species on earth. However, since that energy release now can reasonably be assumed to occur deep underground, and since it "only" created a 100 mile wide by 12 mile deep crater when it occurred at the surface, this might not be a major extinction event. I expect that catastrophic shock waves cause earthquakes and volcanic eruptions worldwide, though. Those dudes in the backyard where it appeared, still have $10^{10}$ gigagwatts to deal with, so they're still insta-fried.

It might be that there are specific lifetimes in this period where the last (most energetic) few seconds of the explosion are close to the surface (bad for humans) or close to the centre of the earth (not so bad for humans).

• 10000 tons: lifetime is now many hours, although it's still sub-proton size. I don't have a model for whether and how it absorbs mass, so I don't know the ultimate fate of the earth. I suspect it doesn't absorb mass, so the earth as a planet is still safe, but I might be wrong. The stuff living on the surface could, as above, be seriously inconvenienced by the general seismic upheaval.

• $2 \times 10^{13}$ kg: radiative power when it appears in the back yard and falls into the ground is now only 1MW, so I guess maybe someone might survive seeing it. Maybe not. Lifetime is "forever", it won't evaporate or explode for all that it's putting out a lot of heat and light. Mass is around 1% that of Mount Everest, so I would think tidal forces become significant (as in Ryan's answer). So, a source of blinding and scorching radiation appears in the back yard, and immediately plummets into the ground. Its mass isn't enough to seriously destabilise the planet, but depending on angular momentum I suppose might approach enough to do something to the earth's rotation and/or magnetic field. I really don't know how quickly it will absorb earth mass -- quite possibly hardly at all, since it's still only the size of an atomic nucleus (yeah, yeah, which element: I don't know!). It at least has the potential to absorb faster than it radiates. In that case earth is doomed, but not necessarily any time soon. We're back to the event being survivable for anyone not in the immediate area (line of sight of where it appears is bad news -- even if it doesn't kill you instantly the X-ray and gamma ray dose is nasty). It's "only" at 6 billion K, so it emits a lot of ionizing radiation, but perhaps nothing that will trouble those with a few km of rock between them and it).

• $6 \times 10^{15}$ kg: Hawking power output is now only 10W, albeit at 20 million K, so that's 10W of X-rays. It becomes a game of exactly where you're standing: you can be torn apart by tidal forces, bashed by infalling matter (stuff in the area will fall towards the black hole, not towards the earth). Infalling matter becomes extremely hot as it approaches the event horizone, and Hawking radiation is no longer preventing stuff from getting near, so the black hole will be steadily fed. But it can only be fed though a small "nozzle" since the black hole is so small, so once it falls out of sight your troubles at least don't get any worse.

• I don't know at what mass the feeding of the black hole deep in the earth becomes a problem for those on the surface. Probably not until the black hole is so large that you're more interested in where so much mass came from (aliens stole the moon?) than what happens to the frankly irrelevant humans ;-)

Note in all this, that there's no option for a black hole to hover in your garden. If it's light enough to be levitated by some incidental effect like electrostatic charge interacting with its earthly surroundings, then it evaporates as close to instantly as makes no difference. If it lasts, it weighs over 100 tons, so it falls. Presumably, whoever manipulated it to be there in the first place has some special uber-technology, and might be able to hold it in place. In which case you have something that's extremely energetic (due to Hawking radiation or infalling matter), and that if massive enough will grab you and slam you directly into its surrounding shell of heated infalling matter, all trying to get through a small gap at once.

Answer 3

Depending on the initial size of the black hole, it would either destroy Earth or be too small and short-lived to even notice.

Black holes lose mass through evaporation. The smaller they are, the faster they evaporate. Less mass means a smaller event horizon and less gravity, which means that they can obtain less new mass. A black hole which loses more mass through hawking radiation than it can consume while in Earths atmosphere would disappears rather quickly.

But when a black hole is large enough and has a constant source of mass which exceeds the loss of mass through evaporation, it will grow. The more it grows, the higher its gravity and the larger its event horizon which means it can absorb even more mass. That means the amount of mass it absorbs increases exponentially.

This handy calculator can be used to calculate the lifetime and other properties of a small black hole with a given mass. It does not take the amount of consumed mass into account, but when you play with it a bit you will soon notice that a black hole with a visible event horizon radius and enough mass to have a notable gravity would be far over the point of equilibrium.

A black hole is affected by gravity. When it appears, it will immediately fall down (or the earth falls up, depending on your frame of reference). Anything which touches the event horizon of a black hole becomes part of the black hole. That means the black hole will not stop when it impacts the ground. It will continue falling downwards towards the center of the earth, consuming any mass which touches its event horizon.

So when the black hole is large enough to see, the kids will only have a very short time to notice it.

Answer 4

First of all, if the black hole is not actually in orbit around the Earth (or, technically, both it and the Earth in orbit around their common center of mass) then, as other commenters have said, it will fall through the Earth, pop out the other side, oscillating back and forth, eating whatever particles it comes into contact with. One of two things could happen, depending on how big it is to start with: either it doesn't eat enough matter fast enough to keep from eventually evaporating, or it does eat enough matter to keep from evaporating, in which case it starts growing larger, unstoppably, and eventually consumes the Earth.

To get a handle on black hole sizes, a black hole the mass of the Earth would be about the size of a golf-ball, and would probably not evaporate for billions of years. A black hole that evaporates in a few seconds or minutes might have the mass of an aircraft carrier, and be a millionth the size of a proton. Caveat: When you discuss things that small, quantum mechanical effects come into play, and the relationship between quantum mechanics and relativity is still poorly understood.

Let's assume that (1) the black hole is small enough to evaporate in a reasonable time (which means it will be too small to see), and furthermore, that (2) we've found a way to contain the black hole above the ground. There are a couple ways I can think of that might be able to contain a black hole. We've already discounted the idea of placing it in orbit (or placing it near a Lagrange point). But black holes can have an electric charge, so we might be able to use an oppositely-charged electric plate beneath it. Momentum can also be transferred to a black hole, so imagine we can use a sort of relativistic particle fountain to hold it in place. This would be like placing a baseball in a high pressure water fountain to hold it up. Only the baseball is microscopic, and weighs more than an aircraft carrier, and the water fountain is a stream of plasma moving at a substantial fraction of the speed of light. I'm not going to do the math to see if that's plausible, but let's pretend like it is! (Let's also ignore the fact that by feeding the black hole, we are causing it to grow, and prolonging its life, which will probably doom us all.)

Under these conditions, what might happen? With such a small black hole, you're generally not going to feel much acceleration from the gravity unless you get really close (distance TBD), but at some point, very close to it, there will be crushing tidal forces.

What I haven't seen anyone discuss is atmospheric effects. Assuming your black hole isn't contained in a vacuum, it will probably start sucking in the atmosphere. Caveat: I have no idea what happens when a subatomic particle hits an event horizon one millionth its size, but I assume the matter will somehow end up collapsing and compressing into the black hole due to tidal forces. I'm also not sure how quickly the atmosphere (at atmospheric pressure) will be able to "drain" through such a small hole. Given that air has weight, and is attracted by the earth's gravity, the air in a column above the black hole will find itself rushing downward, into the top of the black hole, creating a small low pressure area above it. But as the air rushes in towards the black hole, it will probably exceed the sound-barrier, creating a constant sonic boom, that rumbles like a continuous thunder. Due to the Coriolis effect, it will spiral around the center, like water down a drain, possibly creating a rapidly spinning cyclone of air (think of an extreme low-pressure zone). As the air gets highly compressed towards the center, it will become super-heated, and ionized, which will create an accretion disc. As this plasma ignites in fusion, and approaches the speed of light, it will probably emit considerable radiation.

Again, I'm not sure how pronounced any of these effects will be for such a tiny black hole. If it evaporates quickly enough, its possible that none of this will become very bad, or it might take place on such a small scale that it's hardly noticeable.

Best case scenario: we get an awesome roaring cyclone of plasma that doesn't kill us with radiation, crush us with tidal forces, drain the atmosphere, or eat the earth before it disappears. But that's probably too much to ask for.

Answer 5

Hawking radiation is going to be very nasty indeed:

The tiny ones: Anything under 200 tons is gone in less than a second--and it's a total conversion reaction. Even a millgram black hole goes up as 21 tons of TNT--goodbye house. You might survive the detonation of a microgram black hole.

The energy doesn't suddenly cut off at this point, at a billion tons it's still glowing with hundreds of megawatts—not something it's going to be safe to be anywhere near. (And note that it's coming off mostly as ionizing radiation--absorbing 10 watts/kilogram of that is basically certain death.) Even at a trillion tons prolonged exposure isn't healthy.

The second threat is the energy coming off the accretion disk. I'm out of my depth here, though, I'm not sure if there's a range where it's cool enough that you don't fry from the Hawking radiation and also don't fry from the disk. I strongly suspect there is no such range but I do not know.

Thus I would say your answer is a black hole so small that its boom isn't dangerous.

Answer 6

Any black hole small enough to fit a backyard will evaporate in a part of a millisecond.

As such, the survivability of the black hole solely depends on its mass, which will be totally converted into radiation and heat.

In a small atomic bomb about a kilogram of mass converted into radiation and heat. So your black hole should have less than micro-gramms mass.