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

I ran this by my friend awhile ago and I'm not sure how to feel about it still... Consider the following:

We know

[tex]

\nabla_\alpha G^{\alpha\beta}=0\implies \partial_\alpha G^{\alpha\beta}+\Gamma^{\beta}_{\gamma\delta}G^{ \gamma \delta}+\Gamma^{\delta}_{\delta\gamma}G^{ \gamma \beta}=0

[/tex]

Then is it possible to take as the definition of the divergence of the SEM as

[tex]

\partial_\alpha T^{\alpha\beta}=-(\Gamma^{\beta}_{\gamma\delta}G^{\gamma\delta}+ \Gamma^{\delta}_{\delta\gamma}G^{\gamma\beta})?

[/tex]

This seems so to me since if I were clairvoyant I would know that [itex]\mathbf{G}=\mathbf{T}[/itex]. Anyways, given that, I have

[tex]

\partial_{\alpha}G^{\alpha\beta}-\partial_{\alpha}T^{\alpha\beta}=\partial_{\alpha}(G^{\alpha\beta}-T^{\alpha\beta})=0

[/tex]

Now, is there a way to know if the divergence of something being zero implies that the something is zero in order to justify the final step [itex]\mathbf{G}=\mathbf{T}[/itex]?

Thanks,

**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!

# Deriving EFE from the Bianchi Identities

Loading...

Similar Threads for Deriving Bianchi Identities |
---|

I Example of the use of the Lie Derivative in Relativity |

I Lie and Covariant derivatives |

I Riemann curvature tensor derivation |

A Commutator of covariant derivative and D/ds on vector fields |

A Derive the Bianchi identities from a variational principle? |

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