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At what mass is Hawking Radiation a significant factor? Toss something over that either hoovers up your planet, or bakes it if a near miss. Tricky to store, t
by Roboprog 7y ago
At what mass is Hawking Radiation a significant factor?
Toss something over that either hoovers up your planet, or bakes it if a near miss. Tricky to store, though.
- DuskStar 7y agoHawking Radiation is only a significant factor at far lower masses than the Earth. There's a nice calculator here [0], with an example 10^12 kg black hole producing ~350 megawatts. Working backwards, 1 megaton per second (4x10^9 megawatts) gives us a black hole of 3x10^8 kg. 0: http://xaonon.dyndns.org/hawking/ http://xaonon.dyndns.org/hawking/
- contravariant 7y agoAlthough that pretty much means that Hawking radiation very much is a significant factor on any humanly achievable mass.
- DuskStar 7y agoAnd puts some hard, theoretical limits on using black holes as total conversion reactors. Reducing the power output to a terawatt requires 2x10^10kg... Probably not practical. (It would also have a radius of 0.03 femtometers. A proton? ~0.84)
- Roboprog 7y agoIs there a Planck constant type value for minimal singularities?
- philipov 7y agoThe mass of the smallest-possible black hole is called the Planck Mass (~21 micrograms). Such a black hole would have a Schwarzschild radius of 1 planck length, and would evaporate in 1 planck time. The planck mass is also considered to be the largest-possible mass of an elementary particle. https://en.wikipedia.org/wiki/Planck_mass https://en.wikipedia.org/wiki/Planck_mass
- ClumsyPilot 7y agoYou are looking at something that weighs less than mount Everest and thinking that's an unrealistic amount of mass to control. In actual fact, moving mount Everest To The Moon is trivial in comparison with the task of creating a black hole. It's a feat only accessible to Kardashev type 2, at the very least 1.5, civilisations. We are talking about civilisations that can move small planets at will. The most credible approach is to build giant gamma-ray lasers, and focus so much energy into a spot to small, that the weight of light itself will collapse the spot into a tiny black hole made of pure energy, Kugelblitz. Once you would have a black hole formed that way, you could continue force-feeding it with lasers or particle beams to weigh whatever amount you desire. It would be a very energy-inefficient process. At some point the black hole reaches a mass where it's Eddington limit allows it to feed by 'normal' means faster than it evaporates by hawking radiation. At that point it could server to convert matter to energy.
- Roboprog 7y agoSounds like fusion: there’s a big gap between making it happen for a moment and actually using it. ... Ignoring the HUGE gap between smashing together a few atoms so a small fraction of their bits evaporate and smashing them so hard they pretty much disappear.
- perl4ever 7y agoI love that calculator. I asked "so if I want to use a black hole to replace a 60 watt light bulb, how much mass do I need?" And the answer is, roughly that of Phobos. It would also last over 10^22 years, so it might even be cost effective!
- DuskStar 7y agoAnd unlike your standard light bulb, there's no need to worry about it getting dimmer with time - this one'll keep getting brighter until it disappears entirely!
- sbierwagen 7y agoManufacturer's notice: the event horizon temperature goes up as well. By the time it has just five thousand years left, it'll be radiating super-energetic x-rays at (an average) 1.57 giga-electronvolts each. https://arxiv.org/pdf/0908.1803v1.pdf#15 https://arxiv.org/pdf/0908.1803v1.pdf#15
- perl4ever 7y agoYeah, but that's after about ten trillion times the current age of the universe. For the next few billion years, it's going to remain 60 watts.
- Roboprog 7y agoHow would you detect something like that? A primordial black hole the mass of a small asteroid with a tiny absolute magnitude? If such a thing existed, there would likely be more than 1. How long would it take such an object to consume a star like our sun if it grazed or hit the star, vs a harmless hyperbolic flyby?
- sbierwagen 7y agoHere's a Hawking radiation calculator that you can use to get an idea of some of the numbers involved: https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator https://www.vttoth.com/CMS/physics-notes/311-hawking-radiati... Using this calculator, we find that a black hole with the mass of 433 Eros, 6.687E15 kg, would be quite hot, some 18 million kelvin, but emitting just 8 watts of power, and be 0.009 nanometres in radius. Pretty hard to find. Let's try something smaller. 162173 Ryugu, the rock that Hayabusa2 landed on, is only 4.5E11 kg. This gives you a much brighter hole: 1758 megawatts at 2.72657E11 kelvin. Interestingly, this may make it harder to detect! Its blackbody emission peak is at 9,211 KeV, and the Chandra X-Ray observatory only goes up to 10 KeV. (Focusing very-high-energy photons is not easy) You'd have to detect it from the fraction of total power it emits lower down in the spectrum.
- perl4ever 7y agoQuestion: Suppose I wanted to replace my apartment with a black hole. I need about 1300 square feet of area, so how much mass do I need? Answer: About 350 earth masses. Question: After thinking about it, living on a black hole is clearly impractical, but what if I want to replace my heating system with one? What size black hole will produce a comfortable temperature of 70 F? Answer: Roughly the mass of Ceres. Question: I want to go see what an event horizon looks like up close, so what size black hole is needed for the gravity to be 1G at its "surface" for optimal sightseeing? Answer: About a trillion solar masses. It might be a little tricky finding or making one that large, as the largest known in galaxy centers are on the order of 10^10, not 10^12.
- deleted 7y ago[deleted]
- ars 7y ago> to be 1G at its "surface" This doesn't make any sense to me. By definition at the event horizon gravity is enough to keep light from escaping. Light can easily escape from 1G.
- vkou 7y agoIt can escape from a local 1G gravity if the black hole were as small as the Earth. As soon as you move 6400 km away, that 1G gravity turns into 0.25G. But the event horizon of such a black hole would be far larger than that of the Earth. Move 6400 km away, and you'll still have a gravity of ~1G. Rinse and repeat, and you'll find that even light won't be able to escape.
- perl4ever 7y agoThe handy calculator says 1G at the event horizon implies a radius of half a light-year.
- DuskStar 7y agoWhich means it'll be at 1/4G after you travel a further half light year. That's a hell of a lot of energy. (If I'm doing the math right, the potential energy difference is on the order of ~20% of the rest mass at the event horizon)
- perl4ever 7y agoQuestion: Suppose I want to use a black hole to replace a 3 minute egg timer, what kind should I look for? Answer: The appropriate mass is roughly the size of a WWII destroyer, or somewhat more than the largest dump truck in the world. There might be a drawback in that the energy release will be about 50,000 megatons per second. That might affect how fast your egg cooks.
- DuskStar 7y agoEven better way to think of it - the energy release will total that of the mass of a WWII destroyer over the course of three minutes :) Since 50,000 megatons/sec is the starting value, and it'll get bigger as those three minutes count down.
- kabdib 7y agoI wonder how far away you need to be from that thing to survive its last few seconds. Is a few million miles and maybe a good-sized moon to hide behind sufficient?
- ssivark 7y agoA note for this and other comments below. Hawking radiation is more violent (energetic) for smaller black holes. Galactic black holes emit radiation at a much smaller temperature (roughly inversely as mass) while tiny black holes are very hot and evaporate quickly in a runaway “explosion”. However, note that this is only the temperature. The surface area of the BH event horizon (which emits the radiation) scales as mass^2 — that should determine the number of photons/particles.