Rescattering corrections and self-consistent metric in Planckian scattering

Starting from the ACV approach to transplanckian scattering, we present a development of the reduced-action model in which the (improved) eikonal representation is able to describe particles’ motion at large scattering angle and, furthermore, UV-safe (regular) rescattering solutions are found and incorporated in the metric. The resulting particles’ shock-waves undergo calculable trajectory shifts and time delays during the scattering process — which turns out to be consistently described by both action and metric, up to relative order $R^2\mathrm{/}{b}^2$ in the gravitational radius over impact parameter expansion. Some suggestions about the role and the (re)scattering properties of irregular solutions — not fully investigated here — are also presented.