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This question is mostly about a strange seeming similarity that I've noticed between the nature of the weak force and the nature of black holes, which seems to imply that even some astrophysical black holes might be able to interact significantly with the weak force:

Only left-chiral fermions and right-chiral antifermions participate in weak interaction. Even though I know that "spin" or "quantum angular momentum" is not actually believed to involve particles spinning on their axes, I have heard people say that it "really is" angular momentum. As I understand it, the justification for this claim comes primarily from the fact that electrically charged particles with spin create magnetic fields in the same way that they would if they were literally spinning (more-or-less, at least). (I suppose this might also apply to any affects relating to the nuclear strong or weak forces that spinning would cause, though I don't know anything about that.)

Moreover, the quantities of "weak isospin" and "weak hypercharge", which apparently are important for describing how particles interact with the weak force, are related to spin, chirality, and electric charge.

The explanation that I heard of why the weak force is weak (from Don Lincoln) is that it is because the virtual W and Z bosons that "mediate" it have average masses that are very high — far higher than the mass of most elementary particles. This means that the only way that most elementary particles can emit one of these particles is if they the emit one which randomly has an extremely small mass for the short amount of time that it exists, as allowed by the Heisenberg Uncertainty Principle. One thing that this explanation implies is that the weak force is stronger for elementary particles that have higher masses, at least until that mass becomes higher than any of the likely masses for W and Z bosons, and, in fact, the weak force is apparently the strongest force for top quarks, which is why they decay so quickly.

Thus we have that the weak interaction of elementary particles (and I'm not sure if it really is just elementary ones; that's just all I've definitively heard about) is determined by the "mass", "angular momentum", and electric charge of those particles. By strange coincidence, "mass", "angular momentum", and electric charge are exactly the properties that black holes can have according to the "No Hair Theorem". This is the primary impetus for my question: "Can black holes interact with the weak force?"

It seems to me that the fundamental question being asked here is whether the "mass" and "angular momentum" are really somehow the same in both cases. (It seems quite likely to me that they are not, which would tend to doom this idea of black holes acting like elementary particles.)


There are also a few other things that must be considered to fully answer the title question:

If we come to the conclusion that the "angular momentum" that matters for weak interaction is fundamentally different than the frame-dragging "angular momentum" of black holes, then we still have to contend with the fact that lots of left-chiral fermions fell into the black hole, so one might expect the spin to add up like it does in baryons, atoms, etc., (unless, of course, nothing ever falls into a black hole in a way that is meaningful to outside observers, and everything is effectively just sitting there ridiculously time-dilated on the black hole's surface).

This is really just part of the question of how the No Hair Theorem combines with Quantum Field Theory. It seems to me that, according to QFT, all quantum fields should extend out infinitely across space, just like the electromagnetic and gravitational fields. The only differences being that some (particularly color charge) are always pretty completely canceled out by other charges over any non-tiny distance, and others (like the weak force and nuclear force) fall off at a much faster rate than the inverse square law of electrical and gravitational forces over long distances, but crucially never become zero.

These differences make the question of interaction seem pretty esoteric for any macroscopic black hole, since their effects would always be so ridiculously small, but they might matter for micro-black-holes and they might even be related to how information could be imprinted on the surface black holes to avoid the Information "Paradox".

Here are a couple of Stack Exchange questions I found that are specifically about how QFT interacts with the No Hair Theorem: Black Holes and QED , No hair theorem for black holes and the baryon number

There's also the question of whether W and Z bosons could possibly appear as part of Hawking radiation, as well as the question of whether something to do with electroweak theory could make black holes interact with the weak force if they were very small or in very hot environments or formed in a specific way or something.


For reference: I'm fairly familiar with calculus, somewhat familiar with linear algebra, and less familiar with group theory and topology, but most of what I know about physics (and, indeed, about math beyond calculus) comes from YouTube, Wikipedia, and various pop-sci materials.

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    $\begingroup$ I think this question really needs to be pared down some, many are unlikely to actually read through this article to offer up their responses. I do see a good question in here, but it is greatly obfuscated by such a lengthy set-up. $\endgroup$ – Triatticus Jul 29 at 9:56
  • $\begingroup$ Gravi-Weak Unification $\endgroup$ – safesphere Jul 30 at 4:08
  • $\begingroup$ You use a popular bad assumption that things beyond the horizon matter. They don’t. The inner spacetime is causally disconnected from the universe. Whether a BH is hollow or have a “singularity” or magical unicorns inside makes absolutely no difference outside. Any BH effect we can see, such as gravity, charge, or spin, is caused by things outside the horizon. So your question boils down to which properties of matter don’t depend on the speed of time and remain intact in a severe time dilation at the horizon. We know energy, momentum, spin, and electric charge do, but what about weak isospin? $\endgroup$ – safesphere Jul 30 at 4:48
  • $\begingroup$ Exactly. What about weak isospin? $\endgroup$ – H. H. Aug 6 at 1:28
  • $\begingroup$ @Triatticus I guess I should remove most of the background information and just ask the questions. My thinking was that I wanted to avoid trivial answers telling me things I already knew, but your right that it's way too long and trivial answers aren't the worst thing in the world. Also, I've noticed that I ended up asking at least two different questions. I'm not sure whether I should get rid of one or not. I think I'll save the original question somewhere, edit the above text, and then link link to the original in a comment. $\endgroup$ – H. H. Aug 6 at 2:07
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The "No hair theorem" is only a theorem when you consider only gravity and the electromagnetic forces (i.e. it is a statement about vacuum solutions of the Einstein-Maxwell equations.) In the 1970s and 1980s many theorists expected that an generalized no-hair conjecture would also hold: a black hole solutions including weak and strong forces would still be characterized only by the mass, angular momentum, and charges of the various gauge interactions (i.e. electric charge, weak isospin, color charge, etc.)

However, starting in the late 80s it was found that no such generalized no hair conjecture holds when you included non-abelian gauge fields (like the weak and strong force). People showed that when you include these fields, the field equations allow for "hairy" black hole solutions that have zero of the corresponding gauge charges. (E.g. see hep-th/9211007 for a counter example in the case of a spontaneously broken Yang-Mills theorem like the weak interaction in the Standard Model.) This article in Living Reviews in Relativity goes into the current standing of this issue.

So, yes, one would expect black holes to interact with the weak force, however this is more complicated than just assigning a weak isospin value to a black hole. Of course, in Nature the gauge bosons responsible for the weak interaction have mass, consequently, the strength of the weak interaction decays exponentially with distance (this also goes for any related black hole hair). This means that in any realistic scenario the effect of the weak interaction on black holes is completely negligible. (And any situation in which distances would be short enough for the weak interaction to matter would most likely also require a complete theory of quantum gravity.)

PS. Note that there is no (physical) relation between "isospin" and angular momentum. (The name derives from mathematical similarities with quantum theory of spin, and the corresponding group theory.)

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  • $\begingroup$ I think I got the idea that weak isospin and weak hypercharge were related to spin from the fact that they're related to chirality, and I thought that chirality was related to spin somehow. $\endgroup$ – H. H. Aug 26 at 1:11
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Greetings fellow layperson, I would say that my own speculation is yes. I think that it absolutely does. The reason I think so is that the best reason for every particle not being a black hole is naked singularities, and in order for this to be the case, the chargeless, unspinning higgs boson needs to be superextremal, and the only property that it has that is reasonable is isospin and isocharge. Therefore, it is reasonable to assume that the black hole would be able to interact with other things through a force if the force can actually dissolve the event horizon, unless the religion known as string theory is right.

I do think that we should add isospin and isocharge to the hairs, and leave the temperature and wavelength as scales. For microscopic black holes, I would say that the best way to avoid them is to allow them to interact with the weak force.

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