Spectral Characteristic Evolution: A New Algorithm for Gravitational Wave Propagation

Abstract

We present a spectral algorithm for solving the full nonlinear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate spectral characteristic evolution as a technical precursor to Cauchy Characteristic Extraction (CCE), a rigorous method for obtaining gauge-invariant gravitational waveforms from existing and future astrophysical simulations. We demonstrate the new algorithm's stability, convergence, and agreement with existing evolution methods. We explain how an innovative spectral approach enables a two orders of magnitude improvement in computational efficiency.

28 pages, 9 figures

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• Holographic Bubbles with Jecco: Expanding, Collapsing and Critical
• Targeted numerical simulations of binary black holes for GW170104
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• High-accuracy waveforms for black hole-neutron star systems with spinning black holes
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• Summation by Parts and Truncation Error Matching on Hyperboloidal Slices
• Characteristic Formulation for Metric $f(R)$ Gravity
• Parameter control for eccentric, precessing binary black hole simulations with SpEC
• Numerical convergence of model Cauchy-characteristic extraction and matching
• The Bondi problem revisited: a spectral domain decomposition code
• Gravitational radiation by point particle eccentric binary systems in the linearised characteristic formulation of general relativity
• AthenaK simulations of the binary black hole merger GW150914