R β μ ν α = ∂ μ Γ β ν α − ∂ μ ν Γ β μ α + Γ σ μ α Γ β ν σ − Γ σ ν α Γ β μ σ {\displaystyle R_{\beta \mu \nu }^{\alpha }={\partial _{\mu }}\Gamma _{\beta \nu }^{\alpha }-{\partial _{\mu \nu }}\Gamma _{\beta \mu }^{\alpha }+\Gamma _{\sigma \mu }^{\alpha }\Gamma _{\beta \nu }^{\sigma }-\Gamma _{\sigma \nu }^{\alpha }\Gamma _{\beta \mu }^{\sigma }}