Gravitational multipole renormalization

We compute the effect of scattering gravitational radiation off static background curvature, up to second order in Newton constant, known literature as tail and tail-of-tail processes, for generic electric magnetic multipoles. Starting from multipole expansion composite compact objects, expected due quadrupole case, both long- short-distance (UV) divergences are encountered. The former disappears properly defined observables, latter renormalized their associated logarithms give rise a classical renormalization group flow. UV alert incompleteness multipolar description source, not be present UV-complete theory, explicitly derived case conservative dynamics. Logarithmic terms processes multipoles computed this work first time.