Rotating Flat Spacetime in Minkowski Metric

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Discussion Overview

The discussion revolves around the transformation of tetrads in Minkowski spacetime under rotations, specifically focusing on how the metric changes as the coordinate system rotates around the y-axis. The scope includes theoretical aspects of general coordinate transformations and the properties of tetrads in flat spacetime.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about how to adjust the tetrad in Minkowski spacetime as the coordinate system undergoes rotation.
  • Another participant suggests applying the transformation rules for tetrads under general coordinate transformations (gct) and notes that tetrads are determined up to Lorentz transformations, which include spatial rotations.
  • A further contribution proposes starting with a diagonal tetrad in Cartesian coordinates and applying the transformation rule for rotations.
  • Another participant expresses uncertainty about the notation used and recommends writing down the transformation law for the tetrad while parametrizing the rotation with an angle.

Areas of Agreement / Disagreement

Participants appear to be exploring the transformation of tetrads under rotations, but there is no consensus on the specific notation or the exact steps to apply the transformation law.

Contextual Notes

There are limitations regarding the clarity of notation and the specific transformation laws being referenced, which may affect the understanding of the proposed approaches.

parsikoo
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In Minkowski spactime (Flat), if the coordinate system makes a rotation e.g. around y-axis (centred) , for the metric ds^2, how to make the tertad (flat spacetime) as the coordinate system rotats?
 
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You know how the tetrad transforms under a gct. Just apply this transformation rule for rotations. For a given metric the tetrad is only determined up to a lorentz transfo, of which spatial rotations are a subgroup. So you could start with the tetrad components being equal to 1 if you work in cartesian coordinates, and apply the transformation rule.
 
Thanks, you mean:
e(mu)=1 diagonal and for instance put e(24)=-e(42)=omega?
 
I'm not sure about your notation, but writing down the transfo.law for the tetrad and parametrizing the rotation with an angle omega should do it. Just write that transfo. law here and apply the rotation.
 

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