Dark matter, black holes, and hawking radiation, a discrepancy?

So, something I have never seen in scientific talks or papers that I have read, is how dark matter deals with black holes, so, I have some quick questions if this has been addressed.

First I will start with some premises, if any of these are incorrect, feel free to correct them.

We know little about dark matter, we don’t know what interactions it has with normal matter, nor what sort of self interactions it does have. There are two things we do know about it though, the first is that it does not interact with the electromagnetic field, and the other is that is does interact with gravity.

Black holes do not care what kind of matter or energy enters them, it will always result in a larger event horizon, proportional to the mass/energy of the entrant.

Hawking radiation is detectable in the electromagnetic spectrum, and is proportional (inverse exponentially) to the mass.

The Information Conservation law is valid.

Given these premises, what I am having trouble with is figuring what happens to dark matter after it falls into a black hole. According to hawking radiation and information conservation, the dark matter should be reemitted as “dark energy” (which is different from dark energy, but would be the electromagnetic equivalent of dark matter, the long range force (if any) that dark matter interacts with other than gravity.) or dark matter particles. This should not contribute to a temperature detectable by the use of electromagnetic field.

On the other hand, hawking radiation temperature is defined directly by the mass of the black hole and its subsequent horizon.

So, either the hawking temperature needs to be adjusted by the dark matter content of the hole giving a fourth fundemental property of black holes (mass, charge and spin being the original), or dark matter can turn into matter that does interact with the electromagnetic field, which seems it should invalidate the law of information conservation.

Or more likely, I am missing something else that is obvious.

Hawking radiation is usually thought of as electromagnetic radiation simply because because Hawking originally calculated the electromagnetic radiation radiated by a black hole due to the Hawking process. However the same idea can be applied to any other quantum field, though the calculations present more difficulties, therefore Hawking radiation should consist of the entire particle zoo including dark matter.

Of course there is still the problem that. whatever goes into the black hole, the radiation emitted only depends on the mass and angular momentum of the black hole -which is a clear violation of the unitary evolution (i.e. the conservation of information) and is known the black hole information paradox. The BH info paradox is in some ways not too concerning as it seems very likely to simply be an artifact of the semi-classical gravity, but it’s a topic of great interest as it may help to point the way to quantum gravity.

So, would that mean that the actual measured temperature of a black hole would be lower than that calculated naively off the blackbody radiation based on mass?

You invented this rule yourself, there isn’t a theorized kind of energy with the properties you’re thinking of, and nothing in conservation of information would require it. Dark matter, according to most theories, is just matter made up of particles that don’t interact with the electromagnetic force, not something especially exotic.

I did not invent any rule. I asked what would happen, and did give, what I saw, as one possible conclusion. I was just giving an analogy of the long range force that normal matter interacts with that dark matter may interact with, not saying that one does exist. Indeed, given that dark matter is not thought to have much self interaction, it is unlikely that dark matter couples to any long range forces at all.

The conservation of information would require that if the stuff that goes in does not interact with the electromagnetic field, the stuff that comes out should not interact with the electromagnetic field either. Whether those are particles, short range forces, or even, though unlikely, long range forces, they would not be detectable in the electromagnetic spectrum, giving the black hole a lower temperature than one would calculate from simply looking at its mass.

No, it doesn’t - you invented that rule even if you don’t realize you did, it’s not part of any rules of conservation of information that physicists or astronomers use. There simply is no ‘conservation of possibility of interaction with the electric field’ in standard physics. The reason that you’re confused is that you’ve added a conservation rule that physicists don’t believe in, and are wondering why models don’t take that conservation rule into account.

Any given black hole will have a maximum mass of particle it can emit. For any black hole of a size known to exist, the maximum possible mass is sufficiently-low that the only known particles known to be under that mass are photons and gravitons. Neutrinos come in three different masses; the lightest of the three might be light enough (we have no real evidence one way or the other), but the other two are too heavy. Of these, more photons are emitted than gravitons, and if neutrinos are allowed, more of them than photons or gravitons, for subtle reasons relating to the spin of the particles.

But I left a lot of qualifiers in there. Smaller black holes might exist, which could then emit more massive particles (one with the mass of a large asteroid, for instance, could emit all of the neutrinos, electrons and positrons, muons, and pions). And we don’t know the masses of the dark matter particles: Maybe some of them are even lighter than neutrinos (there are reasons to doubt this, but it can’t be ruled out). Black holes wouldn’t care at all about the distinction between dark and non-dark matter, so dark matter particles will be eaten, and if their mass is below the limit of what a hole can produce, they’ll be emitted in Hawking radiation, too.

Also, black holes have very little information themselves, as shown by the “no hair theorems”: They still conserve 4-momentum (including mass, energy, and momentum), electric and magnetic charge, and angular momentum, but nothing else. So no matter whether a hole formed or grew from “normal” matter, dark matter, or any combination, the output of the Hawking radiation will always be the same.

And yes, this does cause problems with quantum mechanics, in that it’s supposed to be impossible for information to be lost. This is one of the current major unsolved problems in physics. The best guess is that the information is still present, but in various correlations of the Hawking radiation, such that you’d need the entire history of all of the radiation from the hole’s entire lifespan in order to be able to recover any of the original information.

If I am understanding you correctly, does this mean a careful measurement of the neutrino Hawking emissions of a black hole could put lower bounds on neutrino masses? As opposed to the upper bounds we currently have.

I did not know that. Thanks.

I thought that had been resolved (I read “The Black Hole War” recently - perhaps Susskind was exaggerating when he described the information paradox as having been settled in that book).

I suppose in principle, but the practical answer is no. Any experiment that could address the question with Hawking radiation could also address it without the Hawking radiation. The problem is that the neutrinos involved would be extraordinarily low energy, and if we could detect neutrinos with energy that low, we would be able to measure their mass directly.

Andy L, whether you consider the question resolved depends on whether you consider that best guess I mentioned to be good enough. I don’t: It’s never been tested experimentally, nor even really validated theoretically (for instance, nothing in the math predicts anything about such correlations or what form they would take). It’s just that it’s the only idea anyone’s come up with that we can’t rule out.


So there is no problem with converting dark matter into electromagnetic radiation? That does solve the problem, but does seem as though some information is lost. It certainly is not practical to get the entire history of the radiation, but it’s also not really practical to take a temperature measurement of a black hoe event horizon either, it’s the principle of the thing, not the possibility of execution. Would you be able to, upon analyzing the entire history of hawking radiation from the hole, be able to tell how much dark matter had fallen into it?

I do realize that information conservation, and really anything to do with quantum gravity or black holes is still unsolved, I believe the current consensus is that information is conserved, but that could change at any time with a new paper. This was just an angle I had not seen explored before, and was curious if anyone had.

That’s the assumption (as well as how many baryons vs. leptons, and any other question you cared to ask), but again, it’s unproven.

EDIT: Oh, and it’s probably also possible (albeit difficult) to convert dark matter into electromagnetic radiation, even without a black hole, provided that all of the other relevant conservation laws are respected. For instance, a neutrino and antineutrino converting to a pair of photons is a valid weak-force process. Though neutrinos are only a small part of the dark matter, and we don’t know what the other parts are or what their weak processes would be, it’s not unreasonable to guess that they might have similar processes.

Sure for a black hole of the sizes observed you wouldn’t expect to find next-to-none massive particles. as the spectrum of Hawking radiation will greatly favour the emission of lower energy particles, but I can’t see any reason for a hard cutoff at such a low energy scale. (of course you may not mean to imply a hard cutoff).

(Sorry if my question is overly foolish.)

Wikipedia agrees: “it does not emit or interact with electromagnetic radiation.”

I guess I see how we know dark matter emits no light — it is dark! :slight_smile: — but how do we know it doesn’t “interact” with EMR?

The easiest example is because it doesn’t seem to absorb light, which is EMR.

Is that because there are no dark blotches in the sky? What if the dark matter is in very tiny clumps of high density?

One of the more common held viewpoints, requires some explanation.
It is not that they are sucked in and lot, just that radially outward becomes inaccessible to them, just as yesterday is an unavailable direction for us.

First of all, black holes aren’t black because they suck everything in, they are black because object near the event horizon are red shifted to the point of becoming undetectable.

Light, particles and teapots that cross the event horizon would appear to slow down and stop for almost the practical lifetime of the universe. That last event, at the event horizon. If we ignore that pesky problem with the infinite redshift, we and all future observers would “see” that information.

This has implication outside of idealized black holes, which do not really describe ones from events like a super massive star collapsing.

The Schwarzschild radius start inside the star, and one thing that is “sucked” in is the remainder of that star. But as it becomes a black hole, with an event horizon inside of that star the star it’self would be frozen just outside the event horizon to an external viewer if it wasn’t for the infinite redshift issue again.

Of course the teapot is not stuck at the event horizon for eternity, the only way that we could observe it actually crossing the event horizon would be for us to cross it ourselves.

It is still a problem for the Copenhagen interpretation, and both theories are incomplete. But basically under the model I was talking about above; if you had infinite time, and could detect infinite red shifted EMR you may be able to get your information back.

I didn’t mean to imply a strict hard cutoff. The energy of the radiated particles has a thermal spectrum, and of course a thermal spectrum doesn’t have a lower cutoff of energy. But it falls off pretty fast, and there’s enough of a gap between most particle masses, enough so that there’s usually no ambiguity about which particles will and will not be emitted to a significant degree.

I still hope someone helps me understand how we know dark matter (which might be very dense) does not absorb light. Don’t make me start another GQ thread just for this! :stuck_out_tongue: