Hyperbolicity of general relativity in Bondi-like coordinates

Gravity seminar at the STAG Research Centre of the University of Southampton.

Date: 22 February 2024

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.

The slides of the seminar can be found here.