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Help! Covariant Derivative of Ricci Tensor the hard way. |
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| Mar3-12, 06:29 PM | #1 |
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Help! Covariant Derivative of Ricci Tensor the hard way.
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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| covariant derivative, einstein tensor, ricci tensor |
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