Constraint propagation in the family of ADM systems

Abstract

The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on "asymptotically constrained" systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of Fourier-component of the constraint propagation equations) are negative or pure-imaginary. We show such a system can be obtained by choosing multipliers of adjusted terms. Our discussion covers Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also mention the so-called conformal-traceless ADM systems.

11 pages, RevTeX, 2 eps figures

Cited by in corpus (21)

• Numerical Relativity and Compact Binaries
• Improved numerical stability of stationary black hole evolution calculations
• Relativistic Hydrodynamic Evolutions with Black Hole Excision
• Numerical Tests of Evolution Systems, Gauge Conditions, and Boundary Conditions for 1D Colliding Gravitational Plane Waves
• Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system
• A cure for unstable numerical evolutions of single black holes: adjusting the standard ADM equations
• Illustrating Stability Properties of Numerical Relativity in Electrodynamics
• Constraint Propagation of $C^2$-adjusted Formulation - Another Recipe for Robust ADM Evolution System
• Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime
• Algebraic stability analysis of constraint propagation
• Constraint propagation equations of the 3+1 decomposition of f(R) gravity
• Theory of gravity admitting arbitrary choice of the energy density reference level
• Axisymmetric Numerical Relativity
• Initial Conditions for Numerical Relativity -- Introduction to numerical methods for solving elliptic PDEs
• On the Hyperbolicity and Stability of $3+1$ Formulations of Metric $f(R)$ Gravity
• Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method
• Constraint propagation in N+1-dimensional space-time
• Gravitational Instability of Yang-Mills Cosmologies
• Constraint Propagation of $C^2$-adjusted Formulation II --- Another Recipe for Robust Baumgarte-Shapiro-Shibata-Nakamura Evolution System ---
• On constraint preservation and strong hyperbolicity
• On the stability of covariant BSSN formulation