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

Abstract

We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et al. [Phys. Rev. D 102, 064035 (2020)] 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—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. [Phys. Rev. D 102, 064035 (2020)]. We discuss a potential application of our formulation for studying gravitational wave scattering.