What happens when a Black Hole completely evaporates?

[jfull]

So, as many of you may know, a singularity will emit Hawking radiation and, in the process, steadily lose mass (provided it isn't taking in mass). They do this because their event horizons disturb Quantum Vacuum Fluctuations, pairs of particles that flash into existence and then annihilate each other. This means that very small singularities will only last a few fractions of a second, due to the large surface area of their event horizons when compared to their mass.

Now, conventional theories assume that black holes evaporate until there is nothing left, but I have to wonder if it might leave some remnant. Is it possible that a singularity could reach so low a mass that its event horizon is no longer large enough to interact with the vacuum fluctuations? (I want to say something like "a radius below the Planck Length", but I honestly don't know enough about that)

Such a singularity would be unable to interact with normal matter, would (probably) be neutrally charged, but would still have some small amount of mass.

And now this is starting to sound like it would fit the definition of Dark Matter.

Obviously, all the black holes that have ever existed wouldn't be enough to produce enough of these singularity remnants to account for the mass of Dark Matter in the universe? Is it possible that they could have been created by the high energies of the first few moments of the Big Bang though? If these singularities are possible, it would be hard to say how many of then might be floating around

Of course, it would be pretty easy to shoot down this idea with some research and a bit of math. It might be that a tiny singularity would not actually have the properties I've described. Also, it may be that a singularity simply cannot have an event horizon that small.

Perhaps I'll do the math to determine what size event horizon would be produced by a singularity with the mass of the lightest elementary particle...

Edited March 16, 2014 by jfull

[sal_vager]

From what I've read (Phil Plait) there's no matter in there anymore to leave a remnant, it's just a point, and once it boils off thanks to Hawking radiation there's nothing left behind :/

[jfull]

From what I've read (Phil Plait) there's no matter in there anymore to leave a remnant, it's just a point, and once it boils off thanks to Hawking radiation there's nothing left behind :/

Yes, but what if there's a point where it can no longer evaporate due to its size?

[sal_vager]

I don't know, also you'd expect the rate of evaporation to go down as the surface area is reduced, but this seems not the case, if anyone can correct me on this please do.

[stupid_chris]

If my memory serves me right, the evaporation is due to the quantum tunneling effect. Current theories predict that it would really fully evaporate, but there's really no way of veryfing any of this as of right now :/

[Z-Man]

Is it possible that a singularity could reach so low a mass that its event horizon is no longer large enough to interact with the vacuum fluctuations?

Conventionally (without quantum gravity), vaccum fluctuations happen at all frequencies and thus have no lowest size limit. Of course, we expect that to be in need of correction once you hit the Planck scale, but that's also the scale where we suspect the final evaporation to take place on... so no, this is very unlikely. It could be that Hawking radiation generation is heavily suppressed in the final stages and that they take longer to decay than simple extrapolation would make you assume, but completely inhibited? Probably not.

[Scotius]

Wait. So does that mean black hole evaporation is 100% efficient method of transforming matter into energy? Whole mass of the star is collapsed into singularity, and with time just evaporates - pouring equivalent of this mass back into the Universe as Hawking radiation. Or is it actually more than that? When one of the quantum particles falls into event horizon it adds its energy to the singularity - so all in all, black holes effectively release more energy than there were to begin with - am i right?

[jfull]

Wait. So does that mean black hole evaporation is 100% efficient method of transforming matter into energy? Whole mass of the star is collapsed into singularity, and with time just evaporates - pouring equivalent of this mass back into the Universe as Hawking radiation. Or is it actually more than that? When one of the quantum particles falls into event horizon it adds its energy to the singularity - so all in all, black holes effectively release more energy than there were to begin with - am i right?

No, it doesn't release more energy than there was to begin with. Also, it doesn't convert all its mass into energy, as much of the radiation it puts out would be in the form of particles (with mass).

That being said, it certainly would be converting some mass into energy, quite a bit of energy.

It would probably outclass fission and fusion, but not be as effective as antimatter annihilation.

However, considering that antimatter will always require amounts of energy equivalent to twice its mass in order to be produced, a singularity would certainly be useful for producing energy (you could just keep "feeding" it controlled amounts of any kind of matter)

Edited March 16, 2014 by jfull

[K^2]

If it had any significant mass to begin with, evaporation ends in a pretty powerful explosion, as the rate at which it increases energy gets exponentially higher as it shrinks. There is absolutely no reason to suspect that evaporation halts, or even slows down, at a certain size.

[Sirrobert]

No, it doesn't release more energy than there was to begin with. Also, it doesn't convert all its mass into energy, as much of the radiation it puts out would be in the form of particles (with mass).

That being said, it certainly would be converting some mass into energy, quite a bit of energy.

It would probably outclass fission and fusion, but not be as effective as antimatter annihilation.

However, considering that antimatter will always require amounts of energy equivalent to twice its mass in order to be produced, a singularity would certainly be useful for producing energy (you could just keep "feeding" it controlled amounts of any kind of matter)

Well that sure would be interesting, if we'd power our FTL spacecraft with controlled singularitys somewhere down the line.

As of right now, I truely do not know enough about this subject to really comment.

But it is a nice thing to concider. Would a miniature singularity even have any effect on the universe?

[K^2]

Except in immediate proximity of the singularity, it would have the same effect as any other object of the same mass.