Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT

We present the first computation of the gauge-invariant, long-wavelength scattering amplitude for the graviton photoproduction by a Kerr-Newman black hole through $\mathcal{O}\big((ωm)^2\big)$, or correspondingly $\mathcal{O}(S^2)$, and to linear order in $G$, using the worldline effective field theory. We show that electromagnetic interactions can be introduced consistently into the spinning worldline theory while preserving spin gauge invariance. We also derive the full angular dependence of the conversion cross section through $\mathcal{O}(S^2)$, and demonstrate that the relevant Wilson coefficients at this order are fixed entirely by matching the electromagnetic and gravitational multipole moments to the Kerr-Newman solution. This result provides a benchmark for future analyses of coupled gravitoelectromagnetic scattering in spinning, charged compact-object backgrounds.