# Rotation tensor and absolute time

• fishnchips
In summary, the conversation discusses the topic of Godel's universe and the question of why a non-vanishing angular velocity makes it impossible to find a three-dimensional hypersurface orthogonal to the world lines of matter. The conversation also mentions papers and resources that may provide further insight on the topic.
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 :)

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

## 1. What is a rotation tensor?

A rotation tensor is a mathematical matrix that represents the rotation of a three-dimensional object around a specific axis. It is used to describe the orientation of an object in space.

## 2. How is a rotation tensor different from a rotation matrix?

A rotation tensor is a higher-dimensional representation of a rotation matrix. While a rotation matrix is a 3x3 matrix, a rotation tensor can have any number of dimensions, depending on the complexity of the rotation being described.

## 3. What is the difference between relative and absolute time?

Relative time is the measurement of time based on the movements and interactions of objects, while absolute time is the measurement of time based on a fixed reference point, such as the rotation of the Earth or the decay of a radioactive element.

## 4. How is absolute time related to the concept of space-time?

Absolute time is one component of the space-time continuum, which combines the three dimensions of space with the dimension of time. In this way, it is a fundamental aspect of how we understand the universe and its physical laws.

## 5. How does the rotation tensor impact our understanding of the universe?

The rotation tensor is a crucial tool in understanding the dynamics of objects in space, from the rotation of planets and galaxies to the motion of subatomic particles. It allows us to mathematically model and predict the behavior of these objects, leading to a deeper understanding of the laws that govern our universe.

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