Rotation tensor and absolute time

[fishnchips]

Hi to all !

I have been doing some research in Godel's universe (I have just finished my first General Relativity course so I'm not an expert yet) and there is something which is still not clear to me. Can someone explain me why the fact of having a non vanishing angular velocity implies that we cannot find everywhere a three-dimensional hypersurface orthogonal to the world lines of matter?

I would really appreciate all your comments :)

 

[bcrowell]

I have been doing some research in Godel's universe (I have just finished my first General Relativity course so I'm not an expert yet) and there is something which is still not clear to me. Can someone explain me why the fact of having a non vanishing angular velocity implies that we cannot find everywhere a three-dimensional hypersurface orthogonal to the world lines of matter?

Are you sure that that's even true? Is the nonexistence of such a surface a feature of all rotating dust solutions, or only of Godel's? E.g., these papers

Su and Chu, http://arxiv.org/abs/0902.4575
Barrow, Juszkiewicz, and Sonoda, http://adsabs.harvard.edu/full/1985MNRAS.213..917B

give rotating cosmological models that are intended to be realistic, unlike the Godel metric. P. 921 of the Barrow paper has some stuff that seems relevant.

 

[George Jones]

Hi to all !

I have been doing some research in Godel's universe (I have just finished my first General Relativity course so I'm not an expert yet) and there is something which is still not clear to me. Can someone explain me why the fact of having a non vanishing angular velocity implies that we cannot find everywhere a three-dimensional hypersurface orthogonal to the world lines of matter?

See sections pages 31 and 32 (pdf page 47) Eric from Poisson's notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf,

which evolved into the excellent book, A Relativist's Toolkit: The Mathematics of black hole Mechanics.

 

[bcrowell]

George, Poisson's treatment goes a little over my head. Is the gist of it sort of similar to the idea that you can't globally synchronize clocks in a rotating frame?

-Ben

 

[fishnchips]

Thanks George ! that made things clearer in my head, great link.

Regards,

Fernando