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Characteristic Evolution and Matching.

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This review traces the development of numerical relativity codes using the characteristic initial-value problem. These codes now enable accurate simulations of black hole mergers and gravitational waves, extending to null infinity.

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Area of Science:

  • Numerical Relativity
  • Computational Astrophysics
  • Gravitational Wave Physics

Background:

  • Numerical evolution codes are crucial for simulating extreme astrophysical phenomena.
  • The characteristic initial-value problem offers a unique approach to these simulations.
  • Cauchy codes have limitations in simulating phenomena up to null infinity.

Purpose of the Study:

  • To review the development of numerical evolution codes based on the characteristic initial-value problem.
  • To highlight the progress and applications of characteristic evolution in general relativity.
  • To discuss the future potential of Cauchy-characteristic matching for global solutions.

Main Methods:

  • Tracing the historical development from 1D to 3D numerical codes.
  • Utilizing Cauchy-characteristic extraction for waveform computation.
  • Exploring Cauchy-characteristic matching for global solutions.

Main Results:

  • Demonstrated progress from 1D feasibility to 2D axisymmetric simulations of relativistic stars.
  • Enabled 3D codes to simulate binary black-hole spacetimes.
  • Successfully extended simulations to null infinity via Cauchy-characteristic extraction.

Conclusions:

  • Characteristic evolution has matured significantly, providing key insights into binary black hole mergers.
  • Cauchy-characteristic extraction allows unambiguous computation of gravitational waveforms.
  • Cauchy-characteristic matching promises to yield global solutions without artificial boundaries.