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The only parameters of a black hole that can be measured from the outside are mass, spin, and charge. E.G. See How can black holes have electric charge and spin?

Other particles have analogs to charge. Quarks and gluons interact through the strong force because they have a color charge. The strong and weak forces are short range, so they would not be expected to have an effect beyond the event horizon.

But what about microscopic black holes? Would the metric be affected by color?


Update 8/2024

A PBS SpaceTime video describes how black holes with a color charge might have formed, and if so how they might be detected. Do Black Holes Have to Be Black?

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  • $\begingroup$ There is no such thing as "microscopic black holes" if you consider the size of the black hole to be the event horizon where even a passing photon would get sucked in. Within the event horizon the actual black hole is typically thought to be a singularity - a point with infinite mass. However there is no good model in physics for what the singularity really is. $\endgroup$
    – MaxW
    Commented Jan 14, 2017 at 18:33
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    $\begingroup$ @MaxW en.wikipedia.org/wiki/Micro_black_hole $\endgroup$ Commented Jan 14, 2017 at 20:59
  • $\begingroup$ @MaxW not a "point with infinite mass", but a point with infinite "density"... in fact a BH has a well defined (finite) total mass. $\endgroup$
    – Quillo
    Commented Mar 21, 2022 at 13:29

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There are reasons why those other quantum charges, like those from the weak and strong force are not able to be hair in a BH. Once inside the horizon BHs that had collapsed with nuclear (strong, weak, or semi strong like nuclear from mesons etc) what those particles were, and their forces, will disappear as information (but see about quantum and soft hair below) See, for the No Hair results for the strong force, for instance,
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.28.452

There's other papers on it.

Classically, in Einstein-Maxwell BHs, nothing else can have hair, under certain restrictions (see the Living Reviews below). It has to do whether the quantity conserved came from a massless local gauge symmetry -- true for mass and charge. If so, then those quantities will be, must be conserved, in an asymptotically flat spacetime. Other entities, such as the dipole moment, or quadrupole moment and so on will either remain as hair, or be radiated to infinity. For electric or magnetic dipole, and higher level electromagnetic multipoles, they can be radiated so do not remain as hair. For gravitational dipoles, they cannot as the lowest multipole that can be gravitationally radiated is quadrupole. Thus, mass angular momentum is one of the hairs of the BH.

The results are that conserved charges or currents of classical or semi-classical fields can only remain as BH hair if they arise from massless gauge fields. Electromagnetism and gravity are spin 1 and 2 gauge fields with zero mass. Flavor and color in weak and strong forces are MASSIVE gauge fields. See some rationale below besides the paper above and the two, Living Reviews and the 1992 Caltech review, below.

One way the no hair theorem sometimes has been stated is that anything that can be radiated will be radiated (I can't immediately find the reference, but multiple papers used the math for it to show similar results). Strong and weak forces do not have quantities that can be radiated to infinity, they're short range (from massive gauge fields) and won't get there. Similarly the symmetry (or approx symmetry) for baryon number or lepton number conservation does not give the BH hair such as baryon number of lepton number. Thus, particle number is not hair, and not 'conserved' in standard General Relativity

See below about soft hair and the Conservation Of information. At this point there is no accepted solution as to how quantum information (such as particle number) could be conserved through the horizon, this remains as the information paradox.

Similarly to electric charge, it is also known that if there are magnetic charges they can also be conserved hair on a BH.

BTW, hair just means you can characterize the BH that way, and it won't change if you leave it alone. But if you interact with it, it can loose charge, angular momentum and mass, and thus energy. That can happen for instance with the Penrose effect, but it requires an external particle(s) or interaction, such as a particle approaching the Kerr horizon and getting into the ergosphere (the particle can emerge with more angular momentum, charge and energy, extracted from the BH, with a conceptual virtiual particles with negative values goes into the horizon). What does get conserved or increases is the entropy. See for instance https://en.m.wikipedia.org/wiki/Penrose_process. It is a way to extract energy from BHs, and it's basically an accepted result, though not yet actually seen.

Now, it is also known that it is possible to have hair from non-classical quantum fileds such as a Yang Mills field, a dilation field, and an axion field. The No Hair theorem gets expanded with some quantum hair being possible. See, for instance,

http://relativity.livingreviews.org/Articles/lrr-2012-7/

http://www.theory.caltech.edu/~preskill/pubs/preskill-1992-quantum-hair.pdf

There is other recent work, by Hawking, Perry and Strominger that BHs have soft hair, and that it may represent the other information that has gone into the BH horizon. Somewhat speculative. That has nothing to do with the weak or strong force, rather with the conformal symmetries at infinity. It's a tentative result they published in early 2016 in arXiv and then in a refereed journal in June. But it is researchers results, others started looking at the issue to see if it makes sense, and if the results, which were simplistic and not fully quantum, hold more generally. See https://phys.org/news/2016-06-hawking-team-soft-hair-theory.html

ADDED REFERENCES AND SUMMARIES FROM PAPERS, ON QUANTUM BLACK HOLE HAIR, SEMI-CLASSICAL HAIR FOR SOLITONS, ON MICROSCOPIC BLACK HOLES (WHICH WILL NEED A QUANTUM GRAVITY THEORY, OR SOME ASSUMPTIONS OF IT)

A paper that claims an Einstein_Yang Mill –Higgs black hole. In a chinese journal, I cant read the paper, the abstract is below. https://www.researchgate.net/publication/241264894_Static_and_stationary_black_holes_with_QCD_hairs ‘The coupled SU(5) Einstein-Yang-Mills-Higgs system of fields is investigated. A family of static spherically symmetric and stationary axisymmetric black hole solutions is obtained. The result shows that the black hole can carry not only the Abelian electric and magnetic charges but also the non-Abelian SU(3)c color charge’

The skyrmion BH, basically a semi-classical BH that has what the author claims is an equivalent to the baryon number. The source is a soliton with a horizon inside the soliton. Part of the abstract is below http://www.sciencedirect.com/science/article/pii/S0550321316303194 ‘We show that the existence of black holes with classical skyrmion hair invalidates standard proofs that global charges, such as the baryon number, cannot be conserved by a black hole. By carefully analyzing the standard arguments based on a Gedankenexperiment in which a black hole is seemingly-unable to return the baryon number that it swallowed, we identify inconsistencies in this reasoning, which does not take into the account neither the existence of skyrmion black holes nor the baryon/skyrmion correspondence.’ From the Coleman and Preskill paper from 1992, in the reference above: The microscopic problems concern the structure of very small ‘In fact the quantum mechanics of black holes presents two sets of problems, with different characters. They might be called the microscopic and the macroscopic problems. The microscopic problems concern the structure of very small black holes, with mass of order the Planck mass. It is difficult, for several reasons, to imagine that the description of such holes (if they exist) would not require a fully developed theory of quantum gravity. The first and simplest reason is that as the mass of a black hole approaches the Planck mass, its Schwarzschild radius 2GM approaches its Compton radius h/M. Thus, irreducible quantum fluctuations in position, which are of order of the Compton radius, render the classical concept of the horizon — or indeed the classical concept of the gravitational field near the nominal location of the hole —problematic.’ See a collection of paper on the hairy black holes (meaning beyond the No hair Theorem) in the literature at http://iopscience.iop.org/journal/0264-9381/page/Focus_issue_on_hairy_black_holes;jsessionid=0C746614346B93500837A3731A1090DD.c1.iopscience.cld.iop.org The first reference is to rotating black holes in asymptotic spacetimes, with non-Abelian gauge fields. It is at http://iopscience.iop.org/article/10.1088/0264-9381/33/23/234002

The abstract says: ‘We here review asymptotically flat rotating black holes in the presence of non-Abelian gauge fields. Like their static counterparts these black holes are no longer uniquely determined by their global charges. In the case of pure SU(2) Yang–Mills fields, the rotation generically induces an electric charge, while the black holes do not carry a magnetic charge. When a Higgs field is coupled, rotating black holes with monopole hair arise in the case of a Higgs triplet, while in the presence of a complex Higgs doublet the black holes carry sphaleron hair. The inclusion of a dilaton allows for Smarr type mass formulae.’

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    $\begingroup$ You have not addressed the "micro" business. Is it covered? "Flavor and color in weak and strong forces are MASSIVE gauge fields" the gluon is massless, and for very high energies (before symmetry breakin) all are massless in a unified theory.l $\endgroup$
    – anna v
    Commented Jan 15, 2017 at 10:45
  • $\begingroup$ @annav - Thank you for that. This answer is worth an up vote. But I was looking at the links and could not find an answer. I presume the answer is no, or the no-hair theorem would mention color. $\endgroup$
    – mmesser314
    Commented Jan 15, 2017 at 15:16
  • $\begingroup$ well here is a preprint theory.caltech.edu/~preskill/pubs/… that seems to be saying "yes" $\endgroup$
    – anna v
    Commented Jan 15, 2017 at 15:53
  • $\begingroup$ The first reference in my answer says color cannot be hair. That leads also to baryon number not being hair. Preskill , also referenced in my answer says that some quantum fields can be hair but does not specifically talk about color. There may not be a QCD Einstein solution or specific result. Understand about very high energies massless qcd, but we don't reach those energies in LHC nor outside horizons in macroscopic BHs. For microscopic, not sure there's a quantum gravity result out. $\endgroup$
    – Bob Bee
    Commented Jan 15, 2017 at 21:29
  • $\begingroup$ Added additional information and references. The microscopic BHs remain a problem, you have to assume a Quantum Gravity theory, as Coleman's paper claims in the reference. Other hairy black holes are referenced, mostly with non-standard fields or idealized ones like Yang Mills SU(2) with Higgs multiplets. There is work on AdS5 spacetime black holes with quark plasma using CFT, but didn't find general results. Scalar hair possible on various cases. Have not found strong or weak force hair. For exotic matter, or violations of the positive energy condition, or quantum hair, still options. $\endgroup$
    – Bob Bee
    Commented Jan 16, 2017 at 4:47

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