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

[Cerenkov]

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.

 

[thierrykauf]

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.

 

[Cerenkov]

Many thanks for this info, thierrykauf!

 

[martinbn]

Carter and Robinson proved it assuming that the space-time has axial symmetry. Hawking removed that assumption, but had an analyticity, assumption which is unreasonable both mathematically and physically. The problem is still open. In the mathematical literature it is known as the rigidity conjecture.

www.ihes.fr/~vanhove/Slides/Klainerman-ihes-fev2011.pdf

https://arxiv.org/pdf/1501.01587

 

[PeterDonis]

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?

 

[PeterDonis]

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.)