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arXiv · 2104.09972

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

Justin L. Ripley
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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.

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Justin L. Ripley. 2021-04-20. A symmetric hyperbolic formulation of the vacuum Einstein equations in affine-null coordinates. https://doi.org/10.1063/5.0055561

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