Rotation tensor and absolute time

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Discussion Overview

The discussion revolves around the implications of non-vanishing angular velocity in Godel's universe, particularly concerning the existence of a three-dimensional hypersurface orthogonal to the world lines of matter. Participants explore theoretical aspects of General Relativity and rotating cosmological models.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on why non-vanishing angular velocity prevents the existence of a hypersurface orthogonal to matter world lines.
  • Another participant questions whether this nonexistence is a characteristic of all rotating dust solutions or specific to Godel's universe, referencing relevant literature.
  • A third participant suggests looking into specific sections of Poisson's notes for further insight into the topic.
  • A participant draws a parallel between the issue and the concept of global clock synchronization in rotating frames.
  • One participant expresses gratitude for the provided resources, indicating a clearer understanding of the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of non-vanishing angular velocity, with multiple viewpoints and references to literature suggesting varying interpretations of the issue.

Contextual Notes

Some discussions reference specific papers and notes that may contain assumptions or definitions that are not fully explored in the thread.

fishnchips
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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 :)
 
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fishnchips said:
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.
 
fishnchips said:
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.
 
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
 
Thanks George ! that made things clearer in my head, great link.

Regards,

Fernando
 

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