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Help! Covariant Derivative of Ricci Tensor the hard way. 
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#1
Mar312, 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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