What Are the Limitations of the No Hair Theorem in Black Hole Dynamics?

[Loren Booda]

"No Hair" theorem?

Why are "No Hair" variables limited to angular momentum (in particular), mass and charge - which together determine the external spacetime of a black hole?

 

[bcrowell]

This is an interesting question. I would love hear any clear conceptual answer that didn't just amount to "because that's what this long, complicated theorem says." One thing to realize is that any answer to your question is going to have to be specific to electrovac solutions. If you put other fields, like axion fields, in there instead of electromagnetic ones, then black holes can have hair.

Here is a review article, which I haven't read: http://relativity.livingreviews.org/Articles/lrr-1998-6/ If you can find a straightforward answer in the article, I'd love to hear about it.

 

[Loren Booda]

The article itself is elegantly simple. It deals with "asymptotically flat, stationary black configurations of self-gravitating classical matter fields." Even very symmetric black holes may have hair. "That the stationary electrovac black holes are parametrized by their mass, angular momentum and electric charge is due to the distinguished structure of the Einstein–Maxwell equations in the presence of a Killing symmetry."

I guess that Schwarzschild black holes may bear a magnetic moment like those of QED. A future step will be to provide experimental evidence, perhaps through asymmetry of orbiting particles or jets. Do any of the hairy fields discussed have a real basis, though?

Other considerations include the effect of hair on Hawking radiation. In my article Black Hole Internal Supersymmetry (on my website through my signature below) I relate a possible influence of the "No Hair" theorem.