Q on Kerr and Kerr-Newman solutions in Straumann's GR

Gold Member
In the book General Relativity by Norbert Straumann, He derives the Kerr's solution in the chapter about black holes and then modifies it to get the Kerr-Newman solution. Then he calculates the g-factor of a rotating charged black hole using the Kerr-Newman solution(and gets the amazing result 2). But all along the way, he calls the gravitating body a black hole. But these solutions aren't only for black holes right? So he only calls the object black hole because he's doing all of these things in the black holes' chapter? If this is correct, so any rotating charged object has g-factor 2 in GR? In contrast to classical physics where there is no g?
Thanks

Matterwave
Gold Member
The Kerr and Kerr-Newman solutions are valid as the exterior solutions only. They do not work on the interior of the object because they are vacuum solutions. However, unlike the Schwarzschild case where good interior solutions are known and match the exterior solutions, I don't believe there has been a good interior solution that matches the Kerr solution. In addition, there's no analogue of Birkhoff's theorem that I am aware of that applies to the Kerr solution. So whereas the Schwarzschild solution describes the exterior of any spherically symmetric and static body, I don't think there's a guarantee that the Kerr solution is the exterior of any rotating , axisymmetric object.

Gold Member
The Kerr and Kerr-Newman solutions are valid as the exterior solutions only. They do not work on the interior of the object because they are vacuum solutions. However, unlike the Schwarzschild case where good interior solutions are known and match the exterior solutions, I don't believe there has been a good interior solution that matches the Kerr solution. In addition, there's no analogue of Birkhoff's theorem that I am aware of that applies to the Kerr solution. So whereas the Schwarzschild solution describes the exterior of any spherically symmetric and static body, I don't think there's a guarantee that the Kerr solution is the exterior of any rotating , axisymmetric object.
About uniqueness theorem, I found these papers which say that Kerr and Kerr-Newman solutions actually are unique. But I haven't read these papers and also from a video lecture on GR, I know they are true under certain conditions and not for all axially symmetric rotating objects.(But its not mentioned in the abstract of these papers!)
http://arxiv.org/pdf/hep-th/0101012.pdf
http://sma.epfl.ch/~wwywong/thesis.pdf
http://arxiv.org/pdf/1208.0294v1.pdf
http://luth.obspm.fr/~luthier/carter/trav/Carter71.pdf

But the fact that there is still no solution for interior of the object that matches Kerr and Kerr-Newman solutions, seems to be a good reason for these solutions being only applicable for BHs...at least yet.
Is it only that interior solutions haven't been found yet, or there is a special kind of peculiarity with them?

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Matterwave
Gold Member
In fact I was just making some comments on the Kerr solution. Comments that I thought may help you in these areas. However, I am far from an expert in this field, so I don't think I can give you much more insight that I already have haha.

ChrisVer
Gold Member
Could a star have a net charge?

ChrisVer
Gold Member
But even if its not possible, I don't have to talk about stars. I can talk about a rotating charged football.

And what kind of "gravitational effects" would you suspect around a football ? They would be highly perturbative/weak... that's why I thought of a star as another stage [apart a black hole] where you could apply the K-N metric.

Gold Member
And what kind of "gravitational effects" would you suspect around a football ? They would be highly perturbative/weak... that's why I thought of a star as another stage [apart a black hole] where you could apply the K-N metric.
Ok, take the Death Star(in Star Wars). I just mean we can imagine something that allows us to assign it a net charge.
Also a weak gravitational field still follows GR. We can choose not to expand!

WannabeNewton