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I was bopping around YouTube and observed this enjoyably produced video. In it, when describing the behavior of a black hole with the mass of a US nickel, the narrator says, "Its 5 grams of mass will be converted to 450 terajoules of energy, which will lead to an explosion roughly three times bigger than the bombs dropped on Hiroshima and Nagasaki combined."

Of all the fun things illustrated there, that was the one whose pretense I didn't understand. Do black holes explode after they've radiated away all of their mass? Or would the "explosion" just come from the rapid pace at which the black hole would consume nearby matter?

The Googling I've done thus far has provided no firm answer. The closest I've come is from the Wikipedia page on Hawking Radiation, which states, "For a black hole of one solar mass, we get an evaporation time of 2.098 × 10^67 years—much longer than the current age of the universe at 13.799 ± 0.021 x 10^9 years. But for a black hole of 10^11 kg, the evaporation time is 2.667 billion years. This is why some astronomers are searching for signs of exploding primordial black holes."

Some other websites refer to the last "explosion" of the Milky Way's supermassive black hole being some 2 million years ago, but is that the same mechanic mentioned on the Wikipedia page? Or the YouTube video, for that matter?

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    $\begingroup$ Just to be clear the "explosion" of the Supermassive black hole is something different. That's jets of energy from in-falling matter. It's not the actual black hole exploding, but matter as it spirals in, gets very hot and releases energy before it falls inside the black hole. $\endgroup$
    – userLTK
    Aug 15, 2016 at 18:18
  • $\begingroup$ Right, that's why I thought the video wasn't likely referring to "friction" or so of the material being consumed. $\endgroup$
    – pdm
    Aug 15, 2016 at 18:29

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What this video is talking about is Hawking Radiation, as you've linked. Hawking Radiation is a proposed hypothetical (by no means verified or proven) way for a black hole to radiate its energy into space. The basic idea is that a black hole is nothing but mass/energy compressed to an infinitesimal point, which is radiating its energy into space over time. For large black holes (such as solar mass or bigger), this radiation process is tiny and the time taken to leak all the black hole's energy into space (and thus for the black hole to "evaporate") is exceedingly long. For tiny black holes however, the time to radiate all the black hole's energy is exceedingly short.

You can calculate how long it will take for a black hole of mass $m$ to evaporate (and release all its mass/energy) with the equation

$$t_{\text{ev}} = \frac{5120\pi G^2 m^3}{\hbar c^4} = (8.41\times 10^{-17}\:\mathrm{s}\:\mathrm{kg}^{-3})\:m^3$$

For $m = 5\:\mathrm{g}=0.005\:\mathrm{kg}$, you get $t_{\text{ev}} \simeq 4\times10^{-19}\:\mathrm{s}$. Now that means in this tiny amount of time, the black hole will radiate all of its mass/energy away and completely evaporate. But the output of all the energy in 5 g of mass is a huge output. Putting out 450 Terajoules of energy in $10^{-19}\:\mathrm{s}$ is basically just an explosion. You can determine the total energy output from the famous equation

$$E=mc^2$$

Just plug in $m = 0.005\:\mathrm{kg}$ and $c = 3\times 10^8\:\mathrm{m/s}$ and you'll get $E=4.5\times 10^{14}\:\mathrm{J} = 450\:\mathrm{Terajoules}$.

So in short, hypothetical calculations (not even theory at this point) suggest that a tiny black hole with the mass of a nickel would immediately explode out in a huge amount of energy. Whether such a black hole can form, or if such an evaporation would/could occur is still highly debated and ultimately unknown at this point.

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    $\begingroup$ @musasabi Actually, Hawking radiation may not be so hypothetical. This just in (French): A researcher at Technion in Israel managed to produce a "sonic" version of a black hole in a Bose-Einstein condensate and showed waves which acted as Hawking radiation, and behaved as expected of such, including exhibiting quantum effects. $\endgroup$
    – Iwillnotexist Idonotexist
    Aug 15, 2016 at 18:52
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    $\begingroup$ @IwillnotexistIdonotexist That's certainly an interesting parallel. I have to wonder if a "sonic" black hole is close enough to a real black hole such that the "radiation" observed is a result of the same physics. Interesting nonetheless. Thanks for sharing! $\endgroup$
    – zephyr
    Aug 15, 2016 at 19:24
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    $\begingroup$ For the record, the evaporation time is a statistical quantity. It is the expected value of a random process. In principle there is a non-zero probability that such a tiny black hole could live for billions of years. If vast numbers of them were made in the early universe, then we might statistically expect that there will be ongoing "explosions" as they finally stop winning the survival lottery. Attempts to detect such events have not been successful, to my knowledge. $\endgroup$
    – zibadawa timmy
    Aug 16, 2016 at 10:36
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    $\begingroup$ @zibadawatimmy That isn't really a useful notion. Yes, it is statistical, but there is a statistical chance that if I stand next to a nuclear bomb, that none of the heat or radiation will hit me. There is a statistical chance that a stone statue will wave its hand. These all break the second law of thermodynamics, which is a statistical law. In reality the probability of such events is so close to to zero that it is not worth worrying about. That is the 5$\sigma$ range of lifespans of a 5gram black hole does not extend to "billions of years". $\endgroup$
    – James K
    Feb 8 at 22:25
  • $\begingroup$ @JamesK The point isn't that one specific such object might survive. But that there might have been inordinate numbers of them, such that a many-$\sigma$ event becomes a fait accompli by sheer magnitude. Just as even small stars manage to undergo the p-p chain despite the probabilities being quite small; the sheer number of protons involved overwhelms the low likelihood. When (# of trials) >> (1/probability of event), you're going to see some of those events with high likelihood. For 5g, sure, that probability is still surely too minute, but for the 10^11 kg in the OP? Highly relevant. $\endgroup$
    – zibadawa timmy
    Feb 9 at 10:06
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No black hole can explode, no matter the size. It can radiate energy outside its event horizon, but a proper "explosion" of energy from the black hole itself would have to exceed the speed of light, which is not currently possible.

Also, if an object has the mass of a nickel, it is not a black hole. More specifically, its event horizon is small enough to fit inside its own surface area which is true for all massive objects that are not black holes. In fact, the event horizon of something with the mass of a nickel is literally immeasurably small (although NOT non-existent). Nickels (and other objects of similar mass) do not have enough gravity to form a black hole. I suspect perhaps you are confusing "mass" with "size"...?

However, if a process existed that could turn the mass of a nickel into the energy it embodies (per E=mc^2), then yes, it would be a tremendous amount of energy. The only such process known to exist would be to have an object with half the mass of a nickel interact (touch) an antimatter-object with half the mass of a nickel. The combined mass of the 2 objects would total the mass of the nickel, and would release the appropriate amount of pure energy with no mass leftover.

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  • $\begingroup$ If Hawking radiation exists, black holes can release energy, they can "explode". While there is no known mechanism to form a black hole with the mass of a nickel, there is no reason that such a black hole couldn't exist. Fluctuations in space time in the very early universe could have produced small black holes. $\endgroup$
    – James K
    Aug 15, 2016 at 21:19
  • $\begingroup$ "its event horizon is small enough to fit inside its own surface area" - tell me, how is the surface area of a black hole defined? $\endgroup$
    – user253751
    Aug 16, 2016 at 8:16
  • $\begingroup$ I would have thought that the event horizon is the surface area of the black hole? $\endgroup$
    – James Hyde
    Aug 16, 2016 at 9:29
  • $\begingroup$ Despite the time it would take even a black hole of solar mass to evaporate, it seems to me that it wouldn't evaporate in a linear matter. As the black hole becomes less massive, it would evaporate faster, until it got down to a nickel sized hole, which would then evaporate fast enough to be considered an explosion. $\endgroup$
    – Howard Miller
    Aug 16, 2016 at 15:42
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    $\begingroup$ @JamesK "While there is no known mechanism to form a black hole with the mass of a nickel..." Well, if black holes do evaporate, then any black hole with a mass larger than a nickle will become a black whole with the mass of a nickle at some point :) $\endgroup$
    – Jason Goemaat
    Aug 21, 2016 at 11:56

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