Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I've seen the Kerr metric usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any coordinates which express the Kerr metric in an orthogonal fashion. Is there ANY choice of coordinates that eliminates all cross terms/off-diagonal terms for the Kerr metric?

If not, is it just a fact that you can never find such a coordinate transformation because of the inherent geometry of the Kerr space-time?

share|improve this question
add comment

1 Answer

A static spacetime can be defined as one that is stationary and such that coordinates exist in which the metric is diagonal. It's interpreted as a spacetime that (1) is stationary, and (2) has no rotation. The Kerr metric is stationary and clearly has rotation, so it can't be static, and you won't be able to put it in diagonal form.

share|improve this answer
    
Could you please give a reference that motivates this definition? I'm rehabilitating my GR after 20 years and it sounds as though understanding this definition would be a good foundational thing to know. I'll ask it as a "real" question if it isn't simple a matter of a reference and if it's going to take you a little bit of work to explain. –  WetSavannaAnimal aka Rod Vance Aug 8 '13 at 1:54
    
@WetSavannaAnimalakaRodVance: You could try my own book: lightandmatter.com/genrel . IIRC this definition is the primary one used in Rindler, Essential Relativity: Special, General, and Cosmological, 1979. –  Ben Crowell Aug 8 '13 at 2:53
    
This doesn't seem right. Diagonal metric is not enough for a static spacetime. For example FRWL metric. –  MBN Aug 8 '13 at 12:15
    
@MBN: Oops, thanks for pointing out my mistake. It's also necessary for it to be stationary. I've tried to fix my answer. –  Ben Crowell Aug 8 '13 at 20:04
    
Georges Lemaître says from on high, "Now say three hail marys" :) Thoroughly wonderful book by the way - I can tell you enjoyed writing it a great deal and I was browsing it until the small hours of this morning. –  WetSavannaAnimal aka Rod Vance Aug 9 '13 at 1:07
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.