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Constraint damping in first-order evolution systems for numerical relativity

Robert Owen

  • Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125, USA

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Phys. Rev. D 76, 044019 – Published 23 August, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.044019

Abstract

A new constraint suppressing formulation of the Einstein evolution equations is presented, generalizing the five-parameter first-order system due to Kidder, Scheel, and Teukolsky (KST). The auxiliary fields, introduced to make the KST system first order, are given modified evolution equations designed to drive constraint violations toward zero. The algebraic structure of the new system is investigated, showing that the modifications preserve the hyperbolicity of the fundamental and constraint evolution equations. The evolution of the constraints for perturbations of flat spacetime is completely analyzed, and all finite-wavelength constraint modes are shown to decay exponentially when certain adjustable parameters satisfy appropriate inequalities. Numerical simulations of a single Schwarzschild black hole are presented, demonstrating the effectiveness of the new constraint-damping modifications.

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Phys. Rev. D 76, 044019– Published 23 August, 2007
  • Received 29 March 2007

© 2007 American Physical Society

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