suppose we have unit vector z=(0,0,0,1), we can use it to form a tensor [itex]z^\mu z^\nu [/itex],(adsbygoogle = window.adsbygoogle || []).push({});

it is easy to check that [itex]∂_\μ( z^\mu z^\nu[/itex]=0 in Minkowski spacetime,

now I want to generalize this equation to general curved spacetime, so that

∇μ ([itex] znew^\mu znew^\nu[/itex])=0.

But I am not sure how to find znew, which should be related to the original z.

Any one can help me? Thanks

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Covariant conservation

Loading...

Similar Threads for Covariant conservation | Date |
---|---|

A Commutator of covariant derivative and D/ds on vector fields | Mar 15, 2018 |

A Showing E-L geodesic def and covariant geodesic def are same | Mar 6, 2018 |

A Constant along a geodesic vs covariantly constant | Feb 27, 2018 |

I Contravariant first index, covariant on second, Vice versa? | Feb 16, 2018 |

Is minimal coupling needed for covariant energy conservation? | Apr 3, 2013 |

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