(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I've been given the Bianchi identity in the form

##\nabla _{\kappa} R^{\mu}_{\nu\rho\sigma} + \nabla _{\rho} R^{\mu}_{\nu\sigma \kappa} + \nabla _{\sigma} R^{\mu}_{\nu\kappa\rho} =0##

2. Relevant equations

3. The attempt at a solution

In order to get from this to the Einstein tensor, I've seen online that you perform a contraction so you get the Ricci tensor and go from there. No two of my indices are the same though, can I just relabel an index? How does the contraction work? Apologies, the bottom three indices should be offset to the right but I can't make latex do it.

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Homework Help: Contraction of the Bianchi identity

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**