Graviton-Photon Mixing by a Kerr-Newman Black Hole with Worldline EFT

In black hole perturbation theory, the difficulty in separating electromagnetic and gravitational sectors of the coupled Teukolsky equations has prevented a general treatment of scattering processes involving both electromagnetic waves and gravitational waves in presence of a Kerr-Newman black hole. We present the first computation of the gauge-invariant, low-frequency scattering amplitude for graviton photoproduction by a Kerr-Newman black hole at tree level up to $\mathcal{O}\big((\omega/m)^2\big)$ or $\mathcal{O}(S^2)$ and linear in $\kappa$, using the worldline effective field theory. The relevant Wilson coefficients are determined by matching the graviton and photon one-point functions to the Kerr-Newman solution. We obtain the full angular dependence of the conversion cross section in the presence of spin and comment on the factorization relation between the graviton photoproduction amplitude and the photon Compton amplitude for a classical spinning source. The result provides a benchmark for future analyses of coupled gravitoelectromagnetic scattering in spinning charged compact object backgrounds.