Can Black Holes Have Color? (Script) (Patreon)

The primary characteristic that defines black holes is in the name. Black holes are black. The gravitational pull at the event horizon is so powerful that not even light can escape. In this case, black means absence of light. We also think of black as indicating absence of colour.  But it turns out there is a way to make a coloured black hole—as long as by colour you mean quantum chromodynamic charge. 

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There are two main types of black holes that we definitely know exist. There are the stellar black holes that might be 10-50 times the mass of the Sun. These are the ones left behind when the most massive stars end their lives in supernova explosions—these things are physically tiny on astronomical scales, with event horizons only tens of kilometers across. Then we have the supermassive black holes in the centers of galaxies, weighing in at millions to billions of times the Sun’s mass with radii on the scale of solar systems. Mass seems to be the most important property distinguishing one black hole from another because it determines the size of their event horizon. The rotation of a black hole—its spin—is the next most important because it squishes that otherwise spherical event horizon and drags the fabric of space around a black hole. 

According to the no-hair theorem of Jacob Bekenstein, black holes can have only three properties—mass, spin, and charge. We covered mass and spin, so what about charge? Normally when we think about black hole charge we think about electric charge—the stuff that electrons and protons have and that shocks you when you drag your feet on the carpet then touch a doorknob. Black holes have a hard time holding onto electric charge because they quickly attract the opposite charge from matter in the surrounding universe and neutralize. They are in contact with the cosmic doorknob, if you like.

But the charge in the no-hair theorem doesn’t just apply to the positive and negative electric charge that feels the electromagnetic force. It refers to any of the charges corresponding to one of the fundamental quantum forces. So could there be black holes that hold onto these weirder types of charge?

The most likely candidate is for a black hole to be charged with the so-called colour charge of the strong force. We have episodes on colour charge, the strong force, and the theory describing it—quantum chromodynamics. But in short, the strong force holds quarks together in protons and neutrons, and holds those together in atomic nuclei. There is one type of charge associated with the electromagnetic interaction - electric charge, which can be positive or negative. But there are three types of charge for the strong force. They’re named after colours: red, green, blue, with their “negatives” being anti-red, anti-green and anti-blue. They aren’t actually these colours, but the naming is not an entirely a poetic choice. There’s a deeper correspondence to how visible colours and strong-force colours are related to each other, which we explain in this video.

OK, so the no-hair theorem tells us that black holes can exhibit any of the charges of the fundamental forces then we should be able to have a red or an anti-blue black hole, from a quantum chromodynamic perspective. But could these really exist out there in the universe? And if so, might they have some real influence on the universe that we could detect? According to a study published this May by PhD student Elba Alonso Monsalve and professor David I. Kaiser at MIT. , the answer is yes and yes. Or at least maybe and maybe.

The reason you probably haven’t heard about colour-charged black holes before is because at first glance they shouldn’t exist. I mentioned that electrically charged black holes aren’t really a thing because they neutralize themselves. Colour-charged black holes should be even harder to make. That’s because of something called colour confinement.

In almost all environments in the modern universe it is impossible to observe an isolated color charge, like a single quark. All color charges need to coalesce together to form color-neutral objects, particles called hadrons. So you’ll never see a single green quark—you’ll see a green, a red and a blue quark bound together into a proton or neutron. Or maybe a red and anti-red quark in a meson. The colour combination of these quark composites, or hadrons, will cancel out to zero colour charge. As real black holes grow from consuming these bound particles, they never have a chance to build up colour charge. 

But that doesn’t mean it’s impossible to separate colour charge. Colour confinement works at temperatures below 10 trillion Kelvin. But above that temperature, individual quarks and gluons are no longer bound and can fly around freely in a quark-gluon plasma. In such a plasma it’s possible to have little patches of more green or anti-red or whatever. If we could create a black hole within such a patch we could presumably create a colour-charged black hole. And, as it happens, there was a time when the universe was filled with a quark-gluon plasma, and by chance we expect that in that time many, many black holes may have formed. It may stand to reason that colourful black holes were once the most natural thing in the world.

So, right after the big bang, the universe consisted of an extremely hot and dense soup of matter and radiation. It was also very slightly clumpy—there was a little more matter here, a little less there—fluctuations that pulled on surrounding material due to their slightly higher gravity, causing them to eventually grow into the bumps of the cosmic background radiation, and eventually into galaxies. But here and there the size of the density fluctuations were large enough to grow even more quickly. Quickly enough to form black holes. These first black holes are called primordial black holes. We’ve never found one, but they could be everywhere. Of course we did episodes on PBHs.

Because these things didn’t form from the cores of dead stars, PBHs could potentially have any mass. From as small as 10^-6 grams to as big as hundreds of thousands of solar masses.  If they formed at the massive end they may have been the first seeds of supermassive black holes in the hope of explaining how those things got so big so fast. If at the lighter end they may be a good candidate for dark matter. The mass these things formed at depends on exactly when they formed in the first second-ish after the big bang. If early then there should be lots of smaller PBHs. If later then there should be fewer but larger ones.

OK, so in the extreme conditions of that first second the universe may have made countless black holes. If that black hole generation happened on the early side—in the first one-100,000th of a second—then we have the conditions we need for coloured black holes.

Before 10^-5 seconds the temperature of the universe everywhere was higher than 10^13 Kelvin, which is the temperature at which bound states of quarks can’t exist. So back then the entire universe was filled with free quarks and gluons—what we call a quark-gluon plasma. Although the net colour charge of this plasma was zero, if you zoom in close enough on little patches you would find regions that are randomly a bit more of one colour than the others. And if such regions were dense enough to collapse into a PBH, that would give us our colour-charged black hole.

The scientists behind this new study wanted to figure out whether these colour-charged PBHs might exist, and in what quantities. To determine that they first needed to know when these things formed—remember, it’s the formation time that determines the size of the PBHs, and the size of the PBHs determines whether they are small enough to capture one of these tiny colour-charged regions of the quark-gluon plasma. 

These researchers use another assumption to choose that formation time. I mentioned that some people think PBHs could explain dark matter. But that only works for a narrow range of primordial black hole masses, because our observations have ruled out there being lots of black holes outside this range. That range is roughly between that of a medium asteroid and a small moon, or 10^14-10^19 kg. If PBHs are dark matter then they are in this mass range, and they must have formed between 10^-21 and 10^-16 seconds after the big bang, and this is the formation range the researchers consider.

The universe at that age is well within the quark-gluon plasma period, so PBHs formed then could potentially have colour charge if they were small enough to land in one of these random fluctuations of colour. Unfortunately, most of the PBHs that would have formed at this time, if they formed at this time, would be too big to capture  any considerable amount of net color charge. Such PBHs would have formed color neutral. 

But there’s still hope for coloured black holes. One of the main scenarios for PBH formation does not form all of the black holes with the same mass. Rather there’s a peak mass, and that’s the mass that would contribute the most to dark matter. But there should also be a long tail of smaller and smaller black hole masses that form alongside these. Some of these would actually be small enough to capture significant colour charge. In the scenarios explored by the researchers an enormous number of tiny, coloured PBHs should have been formed alongside the larger, neutral PBHs that would go on to become dark matter.

In order to capture significant colour charge, a PBH would need to have a mass smaller than around 20 tons, which would make its event horizon ten thousand times smaller than a proton. But these things could hold a lot of colour change—more than any other colored object previously studied. In fact, a subset of these colored black holes would form with near maximum possible amount of color charge that black holes can theoretically have: these are called extremal, or near-extremal black holes, in which the internal colour charge counteracts the internal gravitational field to the point of almost nullifying the event horizon. 

We do have one more problem before we can start building our coloured black hole detectors. All black holes leak away their mass over time due to Hawking radiation. The minimum mass black hole that could still be around today is around 100 billion kg. The smaller the black hole, the faster they leak. Any black hole small enough to have significant colour charge would be long gone. In fact, a 20 ton black hole evaporates in one-ten-thousandth of a second.

That doesn’t sound like very long, but compared to the rapidly changing state of the early universe, this was an aeon. It’s something like 100 trillion times longer than the age of the universe at which those PBHs formed. In fact, that 10^-4 second evaporation time would allow those coloured PBHs to exist well beyond the end of the quark-gluon plasma epoch and enter into the era of color confinement when hadrons start to form. That potentially makes them the only colour-charged objects in the universe at that time.

But do they keep that colour charge? I mentioned that electrically charged black holes quickly lose that charge. But for those early colour-charged PBHs we have reason to hope that they maintain their charge. Remember that these things are tiny—less than one ten thousandth the size of a proton. That means they absorb material very slowly. Also, once the colored black hole becomes surrounded by color neutral hadrons after the quark-gluon epoch is over, a cloud of virtual colored particles could form around it from the quantum vacuum and provide screening, and make it behave like an almost color neutral hadron. For one thing it would stop attracting opposite charges, allowing it to maintain its own internal charge for longer.

Also, this screen process could have left an imprint in the form of gravitational waves: although this would probably be too faint and high-frequency to detect with current detectors. Some of these black holes could have also lasted much longer into the era of big bang nucleosynthesis, the next chapter in the history of the universe when the first sight nuclei began forming from protons and neutrons: this period that lasted about 20 minutes is when the majority of the Helium isotopes formed, together with deuterium, tritium and some Lithium. The surviving colored black holes would be the near-extremal ones, the ones with most color, which happen to have a lower Hawking temperature and thus evaporate slower. These might have changed the distribution of hadrons and disturbed the formation of nuclei in such a way that we may be able to find a discrepancy in the ratio of the numbers of light elements generated in that period. This would be the first hint and evidence of this kind that points to any of this having actually happened.

There is one possible way that colour-charged black holes might exist in the modern universe. Some physicists believe that black holes don’t ever fully evaporate, but instead stop when their size  reaches the smallest definable length—the Planck length. These are called Planck relics. Primordial black holes that started out smaller than a trillion kg would now be Planck relics, and if there are enough of them they could also make up dark matter. And, another in a chain of if’s—if everything I just described is the case, then these still-existent Planck relics could potentially have colour charge. That would be great, because there’s almost no way to detect neutral Planck relics. Colour charge may give them an interaction with atomic nuclei, which means we could build a detector. 

As cool as all of this sounds, are these colored black holes actually a real thing? We don’t have direct observational access to that chaotic first fraction of a second. However, the theoretical basis for their formation is solid, and if right could lead to real, observable effects that help us refine our understanding of the early universe. They may even help solve the problem of dark matter. We just need the universe to have started out with a sprinkling of multicoloured holes in its fabric of spacetime.