 Linearized Levi-Civita connection

ID: linearized-levi-civita-connection

About a Cartesian flat background,

Γ_{β γ}^{α} = \frac{1}{2} η^{α ρ} (\partial_{β} h_{γ ρ} + \partial_{γ} h_{βρ} - \partial_{ρ} h_{β γ}) + O (h^{2}) .

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