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It was once thought that black holes were characterized by their mass, charge, and angular momentum. This was known as the no-hair conjecture. More recent work on black hole physics (see here) suggests that other globally conserved quantities such as baryon number, strangeness, etc also characterize a black hole. In other words, black holes may have hair.

My question concerns possible mechanisms for discerning the color of a black hole's hair. Suppose, for example, that a black hole forms from the gravitational collapse of a star composed of anti-matter rather than matter. This black hole should be characterized by a negative baryon number. How could we distinguish between such an anti-matter black hole and one formed from the collapse of regular matter?

Of even more interest, perhaps, is the possibility of a primordial black hole (PBH) formed before matter began to dominate over antimatter in our universe. The LIGO detections of black hole mergers with masses in the range of tens of solar masses suggests that these PBH may be more common than once thought and it is now being suggested that they might constitute the missing dark matter. Such PBH would presumeably have near zero baryon number (bald black holes?). How would we distinguish these from black holes with hair?

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  • $\begingroup$ Are the hairy traits mediated by fields at distance? Can, for example, the baryon number be detected by a test particle the same way electric charge can? I'd think purely intrinsic properties would only be measurable in the radiation burst of the evaporated black hole. $\endgroup$ – Asher Sep 20 '17 at 16:37
  • $\begingroup$ @Asher That's the issue. The force carriers for baryons are not long ranged like the E&M field or gravity. $\endgroup$ – Lewis Miller Sep 20 '17 at 17:07
  • $\begingroup$ Actually the no-hair conjecture it's still believed to be true in GR, for standard matter content, so no baryon number, strangeness, etc. Can you provide a reference to articles stating the opposite? $\endgroup$ – Rexcirus Sep 21 '17 at 3:48
  • $\begingroup$ @Rexcirus I have inserted a link to the paper that stimulated my question. $\endgroup$ – Lewis Miller Sep 21 '17 at 18:06
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    $\begingroup$ The standard no-hair theorems are rigorous mathematical theorems that have been proved. However, they have certain hypotheses that must be satisfied, e.g., that the solution must be electrovac, i.e., GR with an electromagnetic field. The Dvali paper appears to be talking about GR with other classical fields. That may be of theoretical interest, but is probably of zero relevance for astrophysical black holes. Even electric charge is basically irrelevant for astrophysical black holes. $\endgroup$ – Ben Crowell Sep 21 '17 at 22:48
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This post states that Hawking's last research project involved an attempt to invalidate the "no hair theorem." In light of that I thought it would be interesting (as well as a fitting tribute to Hawking) to revisit this question that I asked 6 months ago. The question did not receive an answer but a comment by @BenCrowell served to douse my curiosity. I repeat his comment below:

"The standard no-hair theorems are rigorous mathematical theorems that have been proved. However, they have certain hypotheses that must be satisfied, e.g., that the solution must be electrovac, i.e., GR with an electromagnetic field. The Dvali paper appears to be talking about GR with other classical fields. That may be of theoretical interest, but is probably of zero relevance for astrophysical black holes. Even electric charge is basically irrelevant for astrophysical black holes."

Now that Hawking has weighed in on the subject my curiosity is again aroused. His work suggests that the event horizon may preserve information on many more quantities that mass, spin, and charge and that this is necessary to save quantum mechanics. My interest in asking the question originally was associated with the possibility that black holes might retain the baryon numbers of the objects from which they are formed and the still unanswered question of the nature of the gravitational interaction between matter and antimatter (see "Does Antimatter Fall Up?"). In the admittedly unlikely event that matter and antimatter are found to repel rather than attract, and the similarly unlikely case that black holes do retain a memory of whether they were formed from matter or antimatter, the universe could be very different from what is commonly assumed (matter dominated). I have already outlined some of these differences in my answer to this question where it is suggested that these possibilities could provide explanations for the baryon asymmetery and dark energy enigmas (albeit requiring a revisit of the equivalence principle of GR).

Consider the Hawking radiation that would be emitted from a black hole with a positive baryon number in the situation that matter and antimatter repel rather that attract. Rather than a random emission of electrons and positrons (the case expected for Hawking radiation with hairless black holes), the emission of positrons would be greatly favored and very high energy positrons at that (the energy determined by the mass of the black hole). Should the black hole have formed from antimatter then the Hawking radiation would be dominated by emission of high energy electrons. The likely very high energies of these electrons and positrons could significantly enhance the experimental detection of Hawking radiation. So if black holes do have hair and the ALPHA-g experiment at CERN does show repulsion between matter and antimatter, then the detection of Hawking radiation may not be such a remote possibility after all.

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