Asymptotic behaviour of zero rest-mass fields on radiative space-times

This thesis adresses two distinct subjects. The first part examines the asymptotic behavior of scalar waves in the Vaidya spacetime, describing a spherical white hole evaporating via emission of isotropic dust. The analysis focuses on the regularity of conformal scalar waves at the isotropic boundary (past and future) of the compactified spacetime, depending on the initial data of the conformal field. Additionally, we construct the conformal scattering operator, demonstrating its ability to encode the entire field evolution in the compactified spacetime.These findings rely on energy inequalities and vector field methods.The second part centers on analyzing incoming isotropic curves in the purely radiative Robinson-Trautman spacetimes of type D. In contrast to a previous study on Vaidya’s metric, these curves do not form the past horizon due to the solution’s geometry. The final chapter categorizes these curves, revealing a behavior akin to that observed in Vaidya’s spacetime.

Theses