Gravity seminar - Athanasios Giannakopolous Seminar

Abstract: The characteristic initial (boundary) value problem has numerous
applications in general relativity (GR) involving numerical studies,
and is often formulated using Bondi-like coordinates. Recently it was
shown that several prototype formulations of this type are only weakly
hyperbolic. I will discuss the root cause of this result, as well as
its implications for the well-posedness of the associated PDE
problems. Focusing on applications related to gravitational waveform
modeling, I will also introduce toy models that capture that PDE
structure of GR and explore numerical convergence of solutions to
their Cauchy-characteristic extraction and matching setups.