For asymptotically regular spacetimes, parity-time reversal symmetry of the leading and subleading initial data implies the Weyl scalars Psi2 and Psi1 peel at null infinity with rates 1/r^3 and 1/r^4.
From this we can compute, for example, PT [Ψ1](λ, R, θ, ϕ) = PT [Cabcdlamblcnd](λ, R, θ, ϕ) = Cabcd(−na)(− ¯mb)(−nc)(−ld)(−λ, R, π− θ, π+ ϕ) = Ψ3(−λ, R, π− θ, π+ ϕ)
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From spatial to null infinity: Connecting initial data to peeling
For asymptotically regular spacetimes, parity-time reversal symmetry of the leading and subleading initial data implies the Weyl scalars Psi2 and Psi1 peel at null infinity with rates 1/r^3 and 1/r^4.