Exploring the Limitations of the No Hair Theorem in Black Hole Dynamics

In summary, the "No Hair" theorem states that black holes are only characterized by their mass, angular momentum, and electric charge due to the structure of the Einstein-Maxwell equations in the presence of a Killing symmetry. This theorem is specific to electrovac solutions, but other fields such as axion fields can result in black holes with hair. Further research is needed to understand the implications of hair on black holes, including its effects on Hawking radiation.
  • #1
Loren Booda
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4
"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?
 
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  • #2


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/ [Broken] If you can find a straightforward answer in the article, I'd love to hear about it.
 
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  • #3


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.
 

What is the No Hair Theorem?

The No Hair Theorem, also known as the "no-hair conjecture", is a theoretical concept in black hole physics that states that a black hole is completely characterized by only three fundamental properties: its mass, electric charge, and angular momentum. This means that all other information about the matter that formed the black hole is lost and cannot be observed by an outside observer.

What are the limitations of the No Hair Theorem?

While the No Hair Theorem is a widely accepted concept, it has its limitations. One of the main limitations is that it only applies to classical black holes and does not take into account quantum effects. Additionally, it assumes that black holes are isolated and do not interact with their surroundings, which may not be the case in reality.

How is the No Hair Theorem tested?

The No Hair Theorem is primarily tested through observations and experiments of black holes. Scientists use telescopes and other instruments to study the effects of black holes on their surroundings, such as the bending of light and the emission of radiation. These observations can help determine the properties of a black hole, which can then be compared to the predictions of the No Hair Theorem.

Are there any exceptions to the No Hair Theorem?

While the No Hair Theorem is a well-established concept, there have been some proposed exceptions. One example is the "hairy" black hole, which suggests that certain types of matter may leave an imprint on the black hole's event horizon, providing additional information about the matter that formed the black hole. However, these exceptions are still under debate and have not been definitively proven.

How does the No Hair Theorem impact our understanding of black holes?

The No Hair Theorem has greatly advanced our understanding of black holes and their properties. It has allowed scientists to make accurate predictions and calculations about black holes, which has been confirmed through observations and experiments. However, it also highlights the limitations of our current understanding and the need for further research to fully understand the complexities of these mysterious objects.

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