CONFORMAL SCATTERING AND THE GOURSAT PROBLEM

Abstract

We work on a class of non-stationary vacuum space-times admitting a conformal compactification that is smooth at null and timelike infinity. Via a conformal transformation, the existence of a scattering operator for field equations is interpreted as the well-posedness of a Goursat problem on null infinity. We solve the Goursat problem in the case of Dirac and Maxwell fields. The case of the wave equation is also discussed and it is shown why the method cannot be applied at present. Then the conformal scattering operator is proved to be equivalent to an analytical scattering operator defined in terms of classical wave operators.