Constraint-preserving boundary conditions in the 3+1 first-order approach

Abstract

A set of energy-momentum constraint-preserving boundary conditions is proposed for the first-order Z4 case. The stability of a simple numerical implementation is tested in the linear regime (robust stability test), both with the standard corner and vertex treatment and with a modified finite-differences stencil for boundary points which avoids corners and vertices even in cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong field scenario, the Gowdy waves metric, showing the expected rate of convergence. The accumulated amount of energy-momentum constraint violations is similar or even smaller than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The application of these results to first-order BSSN-like formalisms is also considered.

Revised version, with conclusive numerical evidence. 23 pages, 12 figures

References in corpus (10)

• Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
• Implementation of standard testbeds for numerical relativity
• Implementation of higher-order absorbing boundary conditions for the Einstein equations
• Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates
• Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations
• Linear high-resolution schemes for hyperbolic conservation laws: TVB numerical evidence
• Towards a gauge-polyvalent Numerical Relativity code
• Boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations
• Geometrization of metric boundary data for Einstein's equations
• Gowdy waves as a test-bed for constraint-preserving boundary conditions

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• Boundary Conditions for the Gravitational Field
• The initial boundary value problem for free-evolution formulations of General Relativity
• Constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation in spherical symmetry
• Constraint Propagation of $C^2$-adjusted Formulation II --- Another Recipe for Robust Baumgarte-Shapiro-Shibata-Nakamura Evolution System ---