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Conservation of Baryon Number

  1. Sep 14, 2010 #1
    Something I've always wondered: You throw matter into a black hole, but get half matter and half antimatter out due to Hawking radiation. Or, you throw only protons in, but get positrons out.

    What happened to conversation of Baryon Number? It seems like you could convert matter to anti-matter this way.
  2. jcsd
  3. Sep 14, 2010 #2
    Even without black holes, the standard model of particle physics doesn't conserve baryon number. There are non-perturbative processes in the electroweak sector (called sphaelerons) which violate both baryon number and lepton number conservation. They do, however, (as do all other SM processes) conserve B-L. Charge conservation in Hawking radiation should be sufficient to ensure at least a sort of B-L conservation.
  4. Sep 14, 2010 #3
    Don't forget that black holes do conserve electric charge (black can be charged, after all). So converting a quark into an anti-quark is out of the question.
  5. Sep 14, 2010 #4
    Drop neutrons in, harvest anti-neutrons out.

    Though now it makes me wonder how a charge on a black hole can be localized to some region of the event horizon. Drop in something charged, and the bias in Hawking radiation spreads outward from that spot at the speed of light? Until the other side of the "surface" knows about it, you could say that the BH is charged on one side, right?
  6. Sep 14, 2010 #5
    My understanding is that you get all kinds of particles out, distributed based on mass (more light ones), but a charged BH will preferentially emit particles of that charge. Not only and everywhere, but just more of them on average.

    So, drop neutrons into a BH. Harvest anti-neutrons and throw back everything else. The BH doesn't know what you put in, other than it being electrically neutral.

    B goes down, L doesn't change.
  7. Sep 14, 2010 #6


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    I think it is a fairly well accepted idea that black hole evaporation violates the standard conservation laws of particle physics. See, e.g., Wald, p. 413. It is true that there are some technical points involved. As Parlyne has pointed out, it's conceivable that only B-L is supposed to be conserved, not B and L separately. Also, the no-hair theorems only hold for electrovac solutions; solutions with hair are known for other fields besides the EM field, so we can't necessarily argue that a black hole must lost all memory of its input characteristics other than its mass, charge, and angular momentum.

    It's actually kind of interesting to try to come up with a clear example where the standard-model conservation laws are violated. For example, let's build a black hole out of pure hydrogen, and then toss in one extra electron, so what went in had B-L=-1 and charge=-1. The fields surrounding this black hole are purely electrovac, so it loses all memory of anything other than its total mass, charge, and angular momentum. Now suppose when it evaporates it spits out that charge as a W- rather than an electron. The final state has B-L=0.
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