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3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints

Manuel Tiglio·Luis Lehner·David Neilsen
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Abstract

We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for the associated initial-boundary value problem. The code is first tested with a gauge wave solution, where rather larger amplitudes and for significantly longer times are obtained with respect to other state of the art implementations. Additionally, by minimizing a suitably defined energy for the constraints in terms of free constraint-functions in the formulation one can dynamically single out preferred values of these functions for the problem at hand. We apply the technique to fully three-dimensional simulations of a stationary black hole spacetime with excision of the singularity, considerably extending the lifetime of the simulations.

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Manuel Tiglio, Luis Lehner, David Neilsen. 2004-09-20. 3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints. https://doi.org/10.1103/physrevd.70.104018

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