Uniqueness Theorems in Non-Flat Spacetime

[Max Green]

Hi, I am writing a report on uniqueness theorems and I am at the section for non asymptotically flat spacetime. I know that if we request certain restrictions, there are the existence of certain uniqueness theorems, however for the most part there are (so far) not many and they are hard to find. Why is it so hard to find uniqueness theorems in non flat spacetime. Additionally, no hair theorems are doubted in (anti)-de sitter space, why is this? I'm not sure how to word it but I am sure its to do with fields not flowing to flat spacetime. Thankyou in advance for any information on thin

 

[pervect]

I doubt I'll be able to help, but I can't resist asking - uniqueness of what? I assume there is a unique solution of something, but it's not clear what that something would be from the context.

 

[Max Green]

Ah yes, that’s my bad, black hole uniqueness theorems, I know there are certain cases for black hole unique solutions but I’m wondering what the more general look is, why don’t we have complete understandings like in 4-D flat spacetime. Thanks

 

[PAllen]

Bkrkhoff’s theorem can be generalized to positive cosmological constant, at least, i.e. de sitter space. See:

https://arxiv.org/abs/0910.5194