Phys.org's Magnetic 'balding' of black holes saves general relativity prediction says:

There is a potentially hairy threat to the conjecture, though. Black holes can be born with a strong magnetic field or obtain one by munching on magnetized material. Such a field must quickly disappear for the no-hair conjecture to hold. But real black holes don't exist in isolation. They can be surrounded by plasma—gas so energized that electrons have detached from their atoms—that can sustain the magnetic field, potentially disproving the conjecture.

Using supercomputer simulations of a plasma-engulfed black hole, researchers from the Flatiron Institute's Center for Computational Astrophysics (CCA) in New York City, Columbia University and Princeton University found that the no-hair conjecture holds. The team reports its findings on July 27 in Physical Review Letters.

"The no-hair conjecture is a cornerstone of general relativity," says study co-author Bart Ripperda, a research fellow at the CCA and a postdoctoral fellow at Princeton. "If a black hole has a long-lived magnetic field, then the no-hair conjecture is violated. Luckily a solution came from plasma physics that saved the no-hair conjecture from being broken."

It links to the recent Phys. Rev. Letter Magnetic Hair and Reconnection in Black Hole Magnetospheres

I'm wondering why the duration of a black hole's magnetic field determine if the no hair conjecture is broken or not.

Question: Why would a black hole's magnetic hair being short-lived not violate the no-hair conjecture, but long-lived hair would violate the conjecture? How long is "long-lived"?

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    $\begingroup$ @DaddyKropotkin thanks for the edit! Ideally the bit at the end should be an exact repeat of the title (that's usually how I do it) so if you'd like to edit further to make them match please feel free to do so! $\endgroup$
    – uhoh
    Aug 6 at 19:01

There are multiple no-hair theorems, but in general the/a no-hair theorem has the following structure. It makes some assumptions about the spacetime:

  1. contains a black-hole event horizon

  2. electrovac

  3. stationary

  4. horizon is a single connected component

From these assumptions, the theorem proves that all solutions have a certain form, with some short list of numbers that parametrize them.

In reality, a stationary spacetime is not one in which a black hole can form by gravitational collapse, because collapse involves change over time. However, when a black hole forms, calculations suggest that it always rings down to the Kerr geometry. This ring-down is an exponential process, so any deviation from the stationary state described by the no-hair theorem very quickly becomes completely undetectable.

  • $\begingroup$ I see, mathematical steady-state solutions are believed to be hairless; in the real world things can be transiently hairy. I was going to ask about theorem vs. conjecture but then found this "There is still no rigorous mathematical proof of a general no-hair theorem, and mathematicians refer to it as the no-hair conjecture." $\endgroup$
    – uhoh
    Aug 7 at 0:58
  • $\begingroup$ fyi I've just asked Why do some call the no-hair conjecture the no-hair theorem? $\endgroup$
    – uhoh
    Aug 7 at 1:13

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