Hi, if you perform this coord. transformation on minkowski metric in cartesian coord. (T,X,Y,Z):(adsbygoogle = window.adsbygoogle || []).push({});

T=t , X=x cos(w t)-y sin(w t) , Y=x sin(wt)+y cos(wt) , Z=z

(it is a frame rotating with angul. speed w around the Z axis) then you get this metric (I'm using the +,-,-,- convention):

ds^2=(c^2-w^2(x^2+y^2))dt^2+2w y dt dx-2w x dt dy - dx^2 - dy^2 - dz^2

Try calculating some components of the curvature tensor (or the ricci scalar),what I get is different from zero! Even if it is just flat metric in different coordinates, why? what's the mistake? Shouldn't flatness (Riemann=0) be coord. invariant?

Thanx

Riccardo

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rotating minkowski metric

Loading...

Similar Threads - Rotating minkowski metric | Date |
---|---|

I Exceeding the speed of light (stars seem to exceed c in our Earth's rotating reference frame) | Jan 7, 2018 |

Insights Relativity on Rotated Graph Paper - Comments | Jul 17, 2016 |

Rotation of coordinate system in minkowsky spacetime | Jun 26, 2011 |

Rotation and Minkowski diagrams. | Nov 27, 2009 |

Rotation and Minkowski diagrams. | Nov 26, 2009 |

**Physics Forums - The Fusion of Science and Community**