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Characteristic Evolution and Matching.

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Characteristic Evolution and Matching.

Jeffrey Winicour1,2

  • 1Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, 14476 Potsdam-Golm, Germany.

Living Reviews in Relativity
|February 10, 2017
PubMed
Summary

Numerical relativity uses the characteristic initial value problem to simulate cosmic events. This approach advances from 1D to 3D simulations, enabling accurate modeling of black holes and gravitational waves.

Area of Science:

  • Numerical relativity
  • Computational astrophysics
  • Gravitational wave astronomy

Background:

  • The characteristic initial value problem offers an alternative to traditional Cauchy evolution in numerical relativity.
  • Simulating extreme astrophysical phenomena like binary black holes requires sophisticated numerical techniques.

Purpose of the Study:

  • To review the development and applications of numerical evolution codes based on the characteristic initial value problem.
  • To highlight the progress in simulating relativistic stars and binary black hole systems.
  • To discuss the application of Cauchy-characteristic matching for computing gravitational waveforms at null infinity.

Main Methods:

  • Tracing the evolution of numerical codes from 1D feasibility studies to 2D and 3D simulations.

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  • Utilizing characteristic evolution and Cauchy-characteristic matching techniques.
  • Comparing characteristic evolution with Cauchy codes for binary black hole simulations.

    • Main Results:

    • Demonstrated feasibility of 1D codes, accuracy of 2D codes for stellar collapse, and progress in 3D binary black hole simulations.
    • Cauchy codes successfully simulate binary black hole problems within artificial boundaries.
    • Characteristic evolution, particularly with Cauchy-characteristic matching, enables computation of radiated waveforms at null infinity.

    Conclusions:

    • Characteristic evolution provides a robust framework for numerical relativity, overcoming limitations of artificial outer boundaries.
    • Advancements in numerical codes facilitate accurate simulations of complex astrophysical systems.
    • Future work should focus on refining Cauchy-characteristic matching for precise gravitational wave extraction.