Rotating Flat Spacetime in Minkowski Metric

[parsikoo]

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?

 

[haushofer]

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.

 

[parsikoo]

Thanks, you mean:
e(mu)=1 diagonal and for instance put e(24)=-e(42)=omega?

 

[haushofer]

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.