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Does John Wheeler's conjecture that black holes have no hair apply to electrons?

Can the electrons have some hair that I can't see?

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    $\begingroup$ Would the electron’s $g$-factor of 2.002319 indicate to you that it’s hairy? What about its weak isospin of -1/2? $\endgroup$
    – G. Smith
    Commented Aug 9, 2020 at 0:44
  • $\begingroup$ @G. Smith - It looks like the magnetic moment of a black hole could be identical to an electron, right? en.wikipedia.org/wiki/Black_hole_electron $\endgroup$ Commented Aug 9, 2020 at 1:43
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    $\begingroup$ Well, the electron’s $g$-factor would have to be 2, not 2.002319. The Kerr-Newman solution can explain the 2 but not the 0.002319. $\endgroup$
    – G. Smith
    Commented Aug 9, 2020 at 2:27
  • $\begingroup$ @G. Smith - Only now I understood you. Thank you! $\endgroup$ Commented Aug 9, 2020 at 3:04
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    $\begingroup$ Related: Can black holes interact with the weak force? $\endgroup$
    – G. Smith
    Commented Aug 9, 2020 at 3:23

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In some sense electron's have even less hair then black holes do. Electrons are governed by quantum field theory and the Standard Model. All electrons are quantum excitations of the same quantum field. Therefor, all electrons in the universe are identical. They all have the same mass, same charge, and same spin. There is no freedom.

However, this "baldness" of the electron has nothing to do with general relativity and the no hair theorem for black holes. In fact even if you were to try to describe an electron as a classical charged black hole, the no hair theorem still would not apply to it. The electron's charge is insanely big for its mass. In geometric units, the electron charge is more than 20 orders of magnitude bigger than the electron mass. This means that when described as a Kerr-Newman solution in general relativity, the electron does not describe a black hole, but a naked singularity without a black hole horizon. The no hair theorem in general relativity applies only to solutions with a horizon.

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