TL;DR
This paper reviews the development of characteristic evolution codes in numerical relativity, highlighting progress from 1D to 3D simulations of relativistic phenomena and their application in waveform computation through Cauchy-characteristic matching.
Contribution
It provides a comprehensive overview of the evolution of characteristic numerical codes in general relativity and their application in gravitational waveform extraction.
Findings
Successful 1D feasibility studies
Accurate 2D simulations of relativistic star oscillations
Current 3D codes modeling binary black hole spacetimes
Abstract
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black spacetime. A prime application of characteristic evolution is to compute waveforms via Cauchy-characteristic matching, which is also reviewed.
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