# How massive would a black hole have to be to swallow a person

As I understand it, very small black holes have very small and close event horizons, and wouldn't necessarily pose a gravitational risk (I know they give off huge amounts of energy, but let's leave that aside for the moment). Assuming that our people have advanced alien technology to keep them from being incinerated by the radiation, what is the minimum mass that a black hole would need to be to actually suck a human being into it, and how close would that human have to come to it? Note, the human in question does not have to survive being torn apart by the gravity as they cross the horizon.

• Any black hole will rip apart the human then swallow his bits - this question pretty much boils down to "how small can a black hole get". (Assuming you're not talking about Micro black holes and are referring to stellar black holes) – Aify Mar 29 '16 at 18:48
• This doesn't deserve a down vote, but maybe a move to hard science? – PCSgtL Mar 29 '16 at 18:57
• It might help a lot if you include the ability of the black hole to evaporate or not naturally. Micro Black holes do so too fast to do any damage as i recall. It would be interesting to know about how much mass a black hole would need to survive long enough to suck a human in from short distance away (variable as necessary) but otherwise deal no real damage before becoming harmless. – Ryan Mar 29 '16 at 19:50
• I would argue this could be considered a weapon-design question and as such would be on-topic. B Evett, is that your intent? – James Mar 29 '16 at 19:57
• For someone willing to do the math. It comes down to how fast a microscopic black hole could swallow a person (particle by particle) vs. how fast the black hole is evaporating. The size in which the person would be consumed just fast enough would be the limiting size. I'm guessing we're talking about mid-sized asteroid mass. – Jim2B Mar 29 '16 at 20:42

Strictly speaking, this question as written is probably more suited for Physics.SE rather than Worldbuilding.SE. However, there are some interesting aspects of black holes that make this a rather fun question, so I'm going to go ahead and say a few things about it anyway (and as some have mentioned in the comments, it wouldn't take much of a stretch to make this on topic for WB, so I'll count it).

The theoretical minimum mass of a black hole is the Planck Mass: about 22 micrograms, if you do the conversion. This black hole would have a Schwarzschild Radius (event horizon) of two Planck Lengths (which is about $3.23 * 10^{-35}$ meters) (to the physicists: yes, I'm assuming non-rotating. Get at me). However, there are two problems with this black hole. I'll deal with the more complicated problem first.

All black holes emit something called Hawking Radiation, slowly losing mass. However, the rate at which they emit this radiation (and therefore the rate at which they lose mass) is inversely proportional to the mass of the black hole itself. That means that the bigger the hole, the slower it loses mass - and the smaller the hole, the faster it loses mass. This makes smaller black holes less stable than big black holes. So much less stable, in fact, that our Planck Mass black hole is basically going to evaporate as soon as it forms. We aren't quite sure yet what the lower limit is for a stable black hole (as far as I know).

The other problem is that a mass of 22 micrograms isn't going to exert enough force on anything to even matter. Many people have this idea of black holes as cosmic vacuum cleaners, sucking up stars and spaceships from all across the galaxy. But it's really just gravity, same as any massive object. We can, for all intents and purposes (since we're really just hand-waving this anyway), treat it as following Newtonian Gravity.

So let's set up your situation. You've got a black hole, and you've got a person (say they're large - 100 kg, we're going for a ballpark estimate anyway). Let's suppose, to make the math easier, that the black hole is above the person, not off to the side. That way the only thing we have to take into consideration is whether the force exerted by the black hole is enough to cancel the gravity from the Earth. Say it's three meters above the person, and we can plug into the basic gravity formula, rearrange, and find that the mass of the black hole would be about $1.35 * 10^{10}$ kg (according to WolframAlpha, this is a bit more than twice the mass of the Great Pyramid).

The Schwarzschild Radius of this black hole would be about $2 * 10^{-17}$ meters. Pretty dang small. So small, in fact, that it would be quite easy to grab on to something in the room and pull yourself away. However, this is the bare minimum needed to counteract gravity on Earth, so you could easily make it a few times more massive.

The question, then, is "Is this black hole stable enough to suck the person in, or will it evaporate right away?". Probably stable, actually. It's hypothesized that black holes of around this size formed in the early moments of the universe, known as Primordial black holes. It's believed that of these black holes, those with masses on the order of $10^{12}$ kg are only now completing their evaporation. So if they last on the order of 14 billion years, they're stable enough to consume a person.

• I like your approach, but your calculation of the black hole mass needed for its gravitational force at 3 m to balance Earth's gravitational force is wrong. From your Wolfram Alpha link you seem to have tried to solve GMm/r^2 = 10 m/s^2 for M given m=100 kg and r=3 m, but 10 m/s^2 is an approximation for the gravitational acceleration, not the gravitational force--the force on a 100-kg person would be ma=(100 kg)*(10 m/s^2) = 1000 kg*m/s^2, so you should solve GMm/r^2 = 1000 for M. Alternately you can just cancel the person's own mass out from both sides and solve GM/r^2 = 10 m/s^2 for M. – Hypnosifl Mar 29 '16 at 23:27
• @Hypnosifl Oooh, good catch. This is what I get for being on SE at work between meetings. (I mean, I'm not on SE at work, what?) – John Robinson Mar 30 '16 at 0:06
• Thanks so much! this is very helpful. I didn't even know about PhysicsSE. The reason I chose Worldbuilding was because I'm asking the question as I try to figure out the details of a story I'm working on. But I appreciate the insights! – B. Evett Mar 30 '16 at 3:10
• How did you use Wofram Alpha to find out that 1.35*10^10 kg is the mass of the Great Pyramid? If I try to solve the equation @Hypnosifl suggests for my person - who is more like 50 kg, and reduce the distance to 1 meter, I get 10^12 kg (if I'm doing the math correctly- which is an "if") - I'm curious what that mass relates to. – B. Evett Mar 30 '16 at 3:43
• B. Evett - to solve GM/r^2 = 9.8 m/s^2 for M, multiply both sides by (r^2/G) to get M = (r^2)*(9.8)/G, for r=1 that works out to (9.8)/(6.67408*(10^(-11))) = 1.47 * 10^11 kg, or 1.47 * 10^8 metric tons. According to the estimate here that's just slightly over the mass of all the buildings in Manhattan. – Hypnosifl Mar 30 '16 at 3:57

You'd need a black hole with a mass of about Jupiter to generate an event horizon with a radius of 9.29 feet. If you used Saturn as your black hole mass, you'd get a radius of about 2.769 feet, plenty large enough to eat a person. An Earth massed black hole is just .3492 inches across.

Don't forget that just because the black hole itself is really small, it's gravitational influence is just as substantial as the regular planet. Also, the "surface gravity" near the event horizon will be gargantuan, sufficient to shred anything known to physics. If used as a weapon, far smaller masses will need to be used to prevent unacceptable collateral damage.

Wolfram Alpha has an amazing Schwarzschild radius calculator. I used it to guess and check until I got to mass close to the size that would easily consume a person.

• Thanks, this is really helpful. When you say ""surface gravity" near the event horizon will be gargantuan" how close do you mean? Say we use the Saturn-massed black hole - it is a few centimeters? a few meters? further? – B. Evett Mar 29 '16 at 20:50
• On the surface of earth, we experience 9.8m/s^2 acceleration because we are almost 4000 miles from Earth's gravitational center. The acceleration due to gravity increases as distance decreases. So, the closer you get, the more acceleration you feel. Wolfram Alpha says that if you're just one meter from a point gravity source the size of earth, you'd experience 3.986×10^14 m/s^2. – Green Mar 29 '16 at 20:56
• wolframalpha.com/input/… – Green Mar 29 '16 at 20:58