Soft factors from classical scattering on the Reissner-Nordstr\"om spacetime

We consider perturbations of the $4$ dimensional Reissner-Nordstr\"om spacetime induced by the probe scattering of a point particle with charge and mass moving on an unbound trajectory with an asymptotically large velocity. The resulting classical radiative solutions are the gravitational and electromagnetic bremmstrahlung. We use these classical solutions to derive the universal photon and graviton soft factor contributions at the tree level, which have the same form as noted in the literature. The soft factor expressions enable us to investigate the tail contribution to the memory effect in late time gravitational and electromagnetic waveforms. We find that generically, the contribution from the charge dominates that from the mass in the late time radiation.