- #1
nobraner
- 13
- 0
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 help will be much appreciated.
[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 help will be much appreciated.