Gravitational multipole renormalization

Abstract

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