Help! Covariant Derivative of Ricci Tensor the hard way.


by nobraner
Tags: covariant derivative, einstein tensor, ricci tensor
nobraner
nobraner is offline
#1
Mar3-12, 06:29 PM
P: 14
I am trying to calculate the covariant derivative of the Ricci Tensor the way Einstein did it, but I keep coming up with

[itex]\nabla_{μ}[/itex]R[itex]_{αβ}[/itex]=[itex]\frac{∂}{∂x^{μ}}[/itex]R[itex]_{αβ}[/itex]-2[itex]\Gamma^{α}_{μ\gamma}[/itex]R[itex]_{αβ}[/itex]

or


[itex]\nabla_{μ}[/itex]R[itex]_{αβ}[/itex]=[itex]\frac{∂}{∂x^{μ}}[/itex]R[itex]_{αβ}[/itex]-[itex]\Gamma^{α}_{μ\gamma}[/itex]R[itex]_{αβ}[/itex]-[itex]\Gamma^{β}_{μ\gamma}[/itex]R[itex]_{αβ}[/itex]

Any assistance will be much appreciated.
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