English

A symmetric hyperbolic formulation of the vacuum Einstein equations in affine-null coordinates

General Relativity and Quantum Cosmology 2021-06-04 v2

Abstract

We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et. al. (arXiv:2007.06419) recently showed that the most commonly numerically implemented formulations of the Einstein equations in affine-null coordinates (and other single-null coordinate systems) are only weakly-but not strongly-hyperbolic. By making use of the tetrad-based Newman-Penrose formalism, our formulation avoids the hyperbolicity problems of the formulations investigated by Giannakopoulos et. al. We discuss a potential application of our formulation for studying gravitational wave scattering.

Keywords

Cite

@article{arxiv.2104.09972,
  title  = {A symmetric hyperbolic formulation of the vacuum Einstein equations in affine-null coordinates},
  author = {Justin L. Ripley},
  journal= {arXiv preprint arXiv:2104.09972},
  year   = {2021}
}

Comments

updated to match journal version

R2 v1 2026-06-24T01:22:06.517Z