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Conservative discretization of the Einstein-Dirac equations in spherically symmetric spacetime

Benedikt Zeller·Ralf Hiptmair
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Abstract

In computational relativity, critical behaviour near the black hole threshold has been studied numerically for several models in the last decade. In this paper we present a spatial Galerkin method, suitable for finding numerical solutions of the Einstein-Dirac equations in spherically symmetric spacetime (in polar/areal coordinates). The method features exact conservation of the total electric charge and allows for a spatial mesh adaption based on physical arclength. Numerical experiments confirm excellent robustness and convergence properties of our approach. Hence, this new algorithm is well suited for studying critical behaviour.

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Benedikt Zeller, Ralf Hiptmair. 2006-07-28. Conservative discretization of the Einstein-Dirac equations in spherically symmetric spacetime. https://doi.org/10.1088/0264-9381%2F23%2F16%2Fs17

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