Abstract: The introduction of the Bondi-Sachs formulation was a foundational breakthrough in the understanding of gravitational waves "at" infinity, and to this day formulations of this type are routinely used in numerical relativity for a variety of purposes.
In my talk I will discuss recent work in collaboration with Thanasis Giannakopoulos and Miguel Zilhao concerning the local well-posedness of the characteristic initial boundary value problem employing such formulations.
Surprisingly, we find that these systems are only weakly hyperbolic, meaning that text-book theorems on well-posedness cannot be straightforwardly applied. Finally I will discuss the consequence of this finding in the numerical setting by using simple toy models.