### Explosions of black holes

• 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?

Thanks in advance. =)

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.

Right, that's why I thought the video wasn't likely referring to "friction" or so of the material being consumed.

• zephyr Correct answer

6 years ago

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.

This was a brilliantly succinct and complete answer. Thank you! Also, typo corrected. =)

@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.

@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!

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.

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Content dated before 7/24/2021 11:53 AM

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