Suppose F := 1 − − 2 M ( u ) r , then the Lagrangian for null radial geodesics ( L = 0 , θ θ ˙ ˙ = 0 , ϕ ϕ ˙ ˙ = 0 ) of the "retarded(/outgoing)" Vaidya spacetime Eq(6) is L = 0 = − − F u ˙ ˙ 2 + 2 u ˙ ˙ r ˙ ˙ , where dot means derivative with respect to some parameter λ λ . This Lagrangian has two solutions, u ˙ ˙ = 0 and r ˙ ˙ = F 2 u ˙ ˙ .