For the "retarded(/outgoing)" Schwarzschild metric Eq(3), let G := 1 − − 2 M r , and then the Lagrangian for null radial geodesics will have an outgoing solution u ˙ ˙ = 0 and an ingoing solution r ˙ ˙ = − − G 2 u ˙ ˙ . Similar to Box A, now set up the adapted outgoing tetrad by l a = ( 0 , 1 , 0 , 0 ) , n a = ( 1 , − − G 2 , 0 , 0 ) , m a = 1 2 r ( 0 , 0 , 1 , i csc ⁡ ⁡ θ θ ) , l a = ( − − 1 , 0 , 0 , 0 ) , n a = ( − − G 2 , − − 1 , 0 , 0 ) , m a = r 2 ( 0 , 0 , 1 , sin ⁡ ⁡ θ θ ) . so the spin coefficients are κ κ = σ σ = τ τ = 0 , ν ν = λ λ = π π = 0 , ε ε = 0 ρ ρ = − − 1 r , μ μ = − − r + 2 M 2 r 2 , α α = − − β β = − − 2 cot ⁡ ⁡ θ θ 4 r , γ γ = M 2 r 2 , and the Weyl-NP and Ricci-NP scalars are given by Ψ Ψ 0 = Ψ Ψ 1 = Ψ Ψ 3 = Ψ Ψ 4 = 0 , Ψ Ψ 2 = − − M r 3 , Φ Φ 00 = Φ Φ 10 = Φ Φ 20 = Φ Φ 11 = Φ Φ 12 = Φ Φ 22 = Λ Λ = 0 .