- #1
nobraner
- 13
- 0
Start with
[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}R^{\mu\nu}[/itex]
insert the multiplicative identity, expressed as the product of the covariant and contravariant metric
[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}(g^{\mu \nu}g_{\mu\nu})R^{\mu\nu}[/itex]
contract the indices of the Ricci Tensor, to get
[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}g^{\mu\nu}R[/itex]
but the general theory tells us that
[itex]\nabla_{μ}R^{\mu\nu}=\frac{1}{2} \nabla_{μ}g^{\mu\nu}R[/itex]
Where have I gone wrong?
[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}R^{\mu\nu}[/itex]
insert the multiplicative identity, expressed as the product of the covariant and contravariant metric
[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}(g^{\mu \nu}g_{\mu\nu})R^{\mu\nu}[/itex]
contract the indices of the Ricci Tensor, to get
[itex]\nabla_{μ}R^{\mu\nu}=\nabla_{μ}g^{\mu\nu}R[/itex]
but the general theory tells us that
[itex]\nabla_{μ}R^{\mu\nu}=\frac{1}{2} \nabla_{μ}g^{\mu\nu}R[/itex]
Where have I gone wrong?
Last edited: