Flat-space photon and graviton scattering off a heavy charged source reproduces the exact Moncrief mixing matrix that decouples Reissner-Nordstrom perturbations for every multipole ell >= 2.
The Gordon identity gives Tµν 1/2 = 1 4m ¯u(p′) [ PµPν + i 2 (Pµσνρ +P νσµρ) ∆ρ ] u(p).(C18) The first term is spin even and the second is spin odd
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On-Shell Amplitudes and Black-Hole Perturbations: Exact Reissner-Nordstr\"om Mixing
Flat-space photon and graviton scattering off a heavy charged source reproduces the exact Moncrief mixing matrix that decouples Reissner-Nordstrom perturbations for every multipole ell >= 2.