What is the 'proof' of the no-hair theorem of black holes?

In summary, the no-hair theorem, which states that the only stationary black holes are the Kerr solutions, was proved by the combined work of Israel, Carter, Robinson and Hawking. The theorem was later extended to include an electromagnetic field by Robinson. However, the problem is still open as Hawking's assumption of analyticity is considered unreasonable both mathematically and physically. This topic is at least at an intermediate level and the references provided are at an advanced level.
  • #1
Cerenkov
274
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Hello.

In chapter 3 (Quantum Black Holes) of this book... https://www.amazon.com/dp/069116844X/?tag=pfamazon01-20 ...Stephen Hawking writes...

"The no-hair theorem, proved by the combined work of Israel, Carter, Robinson and myself, shows that the only stationary black holes in the absence of matter fields are the Kerr solutions. These are characterized by two parameters, the mass M and the angular momentum J. The no-hair theorem was extended by Robinson to the case where there was an electromagnetic field. This added a third parameter Q, the electric charge."

My questions concern what Hawking meant by the words, '...proved by the combined work of..'

Is there a single paper where these four scientists worked together to offer up said proof?

If so, could I please be directed to it?

Or, is there somewhere that I can find the proof 'combined' from the work of these four?

Any help given at a Basic level would be appreciated.
Thank you,

Cerenkov.
 
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  • #2
Israel, W., (1967). “Event horizons in static vacuum spacetimes”, Phys. Rev. 164, 1776.
Israel, W., (1968). “Event horizons in static electrovac spacetimes”, Commun. Math. Phys. 8, 245.
Kerr, R. P., (1963). “Gravitational field of a spinning mass as an example of algebraically special metrics”, Phys. Rev. Lett. 11, 237.
 
  • #3
Many thanks for this info, thierrykauf!
 
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  • #5
martinbn said:
an analyticity, assumption which is unreasonable both mathematically and physically

The links you give don't go into any detail about why this is. Is there a simple explanation of why analyticity is unreasonable as an assumption?
 
  • #6
Cerenkov said:
Any help given at a Basic level would be appreciated.

This really isn't a "B" level topic (it's at least "I" and probably "A"--certainly the references given so far are "A").

For that reason, this thread is now closed since the OP has been given references. (I have a further question about the references @martinbn posted, but I'll start a new thread for that.)
 

1. What is the no-hair theorem of black holes?

The no-hair theorem of black holes states that all black holes can be described by only three properties: mass, electric charge, and angular momentum. This means that all other information, such as the matter that formed the black hole, is lost and cannot be observed from the outside.

2. What is the proof of the no-hair theorem?

The proof of the no-hair theorem was first proposed by physicist John Wheeler in 1971 and was later formalized by physicists Stephen Hawking and Jacob Bekenstein. It is based on the laws of thermodynamics and general relativity, which state that black holes have a temperature and entropy proportional to their surface area.

3. How does the no-hair theorem affect our understanding of black holes?

The no-hair theorem has significant implications for our understanding of black holes. It suggests that black holes are simple objects with only three properties, rather than complex structures with unique characteristics. It also supports the idea that black holes have a connection to thermodynamics and information theory.

4. Is the no-hair theorem universally accepted?

The no-hair theorem is widely accepted by the scientific community, as it is supported by mathematical proofs and observations of black holes. However, some physicists continue to debate its validity and implications, particularly in relation to quantum mechanics and the information paradox.

5. How does the no-hair theorem relate to the event horizon of a black hole?

The no-hair theorem does not directly relate to the event horizon of a black hole, but it does support the idea that the event horizon is the only observable feature of a black hole. This means that any information or matter that falls into a black hole is permanently trapped beyond the event horizon and cannot be observed from the outside.

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