First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations

Abstract

We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type allows us to make concrete statements about existence of solutions. In addition, it offers concrete advantages for numerical applications as it now becomes possible to incorporate advanced numerical techniques for first order systems, which had thus far not been applicable to the characteristic problem of the Einstein equations, as well as in providing a framework for a unified treatment of the vacuum and matter problems. This is of relevance to the accurate simulation of gravitational waves emitted in astrophysical scenarios such as stellar core collapse.

arXiv commentrevtex4, 7 pages, text and references added, typos corrected, to appear in Phys. Rev. D

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Cited by in corpus (13)

• Extraction of Gravitational Waves in Numerical Relativity
• Characteristic Evolution and Matching
• Characteristic Evolution and Matching
• A framework for large-scale relativistic simulations in the characteristic approach
• Fully relativistic three-dimensional Cauchy-characteristic matching for physical degrees of freedom
• Hyperbolicity of General Relativity in Bondi-like gauges
• Well-posed first-order reduction of the characteristic problem of the linearized Einstein equations
• Gauge structure of the Einstein field equations in Bondi-like coordinates
• Numerical convergence of model Cauchy-characteristic extraction and matching
• Estimates for the characteristic problem of the first-order reduction of the wave equation
• Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
• Constraint Preserving Boundary Conditions for Hyperbolic Formulations of Einstein's Equations
• On the Linear Regime of the Characteristic formulation of General relativity in the Minkowski and Schwarzschild's Backgrounds