Seminarium Teorii Względności i Grawitacji

The displacement and the non-linear memory effects for Robinson-Trautman waves are explicitly worked out. This is done by constructing the combined frame rotation and coordinate transformation in which Robinson-Trautman waves are manifestly locally asymptoticallyflat at future null infinity. This allows one to apply well-established results on how toderive memory effects in this context. In a second step, we construct a suitably im-proved generalized mass aspect that provides a local Lyapunov function for the flowin the sense that it is manifestly positive. News-free solutions are studied in detailand shown to coincide with the vacuum sector of Euclidean Liouville theory. Theycorrespond to a boosted and rescaled Schwarzschild black hole. As a by-product, weshow that the displacement and non-linear memory effects in locally asymptoticallyflat spacetimes at future null infinity are invariant under supertranslations and covariant under BMS4 Lorentz transformations. A novel interpretation of modified flowsthat control the low harmonics in terms of keeping the system in its instantaneousrest frame is provided.