hello ,(adsbygoogle = window.adsbygoogle || []).push({});

In the Bianchi Identities of the second kind, we have ∇a R_{bcde}+ ∇b R_{cade}+ ∇c R_{abde}≡ 0

but since ∇c R_{abde}= - ∇c R_{bade}

we get :

∇a R_{bcde}+ ∇b R_{cade}- ∇c R_{bade}= 0

in the last term, we exchange the c and the b indices and we would arrive at:

∇a R_{bcde}+ ∇b R_{cade}- ∇b R_{cade}= 0

which leads to :

∇a R_{bcde}= 0 .

but this incorrect ? did I do something wrong ?

I would like actually to arrive at the formula :

2 ∇b R_{acde}− ∇a R_{bcde}≡ 0.

see formula 9 here from original Bel's article from 1938:

http://gallica.bnf.fr/ark:/12148/bp...ction+d'un+tenseur+du+quatrième+ordre;.langEN

and

(see formula 5 here : https://docs.google.com/viewer?a=v&...9JJLhB&sig=AHIEtbRUONCiZUSV_8erdxK9YSMiouUrjA)

Thanks,

cheers,

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

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!

# Bianchi Identity-where did I go wrong?

Loading...

Similar Threads - Bianchi Identity where | Date |
---|---|

A Derive the Bianchi identities from a variational principle? | Oct 5, 2017 |

I What constrains the metric tensor field in GR? | Jul 31, 2017 |

Vanishing of Einstein tensor from Bianchi identity | Apr 7, 2015 |

Bianchi Identity | Mar 9, 2015 |

Bianchi identity with F^ab F^cd | Mar 1, 2014 |

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