Scattering from Infinity of the Maxwell Klein Gordon Equations in Lorenz Gauge

We prove global existence backwards from the scattering data posed at infinity for Maxwell Klein Gordon equations in Lorenz gauge satisfying weak null condition. The asymptotics of solutions to were shown be wave like and homogeneous towards timelike arXiv:1803.11086 expressed terms radiation fields, thus our will given form fields backward problem. give a refinement results arXiv:1803.11086, then making use this refinement, we find solution which attains prescribed infinity. Our work starts approach [22] is more delicate since it involves nonlinearities with fewer derivatives. result corresponds "existence states" theory. method proof relies on suitable construction approximate data, weighted conformal Morawetz energy estimate spacetime version Hardy inequality.