# How could we determine the color of a black hole's hair?

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?

• 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. – Asher Sep 20 '17 at 16:37
• @Asher That's the issue. The force carriers for baryons are not long ranged like the E&M field or gravity. – Lewis Miller Sep 20 '17 at 17:07
• 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? – Rexcirus Sep 21 '17 at 3:48
• @Rexcirus I have inserted a link to the paper that stimulated my question. – Lewis Miller Sep 21 '17 at 18:06
• 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. – user4552 Sep 21 '17 at 22:48