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Conservative Discretization of the Einstein-Dirac equations in spherically symmetric space-time

by B. Zeller and R. Hiptmair

(Report number 2006-06)

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 an spatial Galerkin method suitable for finding numerical solutions of the Einstein-Dirac equations in spherically symmetric space-time (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.

Keywords:

@Techreport{ZH06_355,
  author = {B. Zeller and R. Hiptmair},
  title = {Conservative Discretization of the Einstein-Dirac equations in spherically symmetric space-time},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2006-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2006/2006-06.pdf },
  year = {2006}
}

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