Numerical stability of a new conformal-traceless 3+1 formulation of the Einstein equation

Abstract

There is strong evidence indicating that the particular form used to recast the Einstein equation as a 3+1 set of evolution equations has a fundamental impact on the stability properties of numerical evolutions involving black holes and/or neutron stars. Presently, the longest lived evolutions have been obtained using a parametrized hyperbolic system developed by Kidder, Scheel and Teukolsky or a conformal-traceless system introduced by Baumgarte, Shapiro, Shibata and Nakamura. We present a new conformal-traceless system. While this new system has some elements in common with the Baumgarte-Shapiro-Shibata-Nakamura system, it differs in both the type of conformal transformations and how the non-linear terms involving the extrinsic curvature are handled. We show results from 3D numerical evolutions of a single, non-rotating black hole in which we demonstrate that this new system yields a significant improvement in the life-time of the simulations.

7 pages, 2 figures

References in corpus (2)

• Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
• A cure for unstable numerical evolutions of single black holes: adjusting the standard ADM equations

Cited by in corpus (21)

• Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
• Toward standard testbeds for numerical relativity
• Improved numerical stability of stationary black hole evolution calculations
• On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations
• Exploring New Physics Frontiers Through Numerical Relativity
• Summation by parts and dissipation for domains with excised regions
• Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations
• Moving black holes via singularity excision
• Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system
• Toward stable 3D numerical evolutions of black-hole spacetimes
• Einstein boundary conditions for the 3+1 Einstein equations
• Impact of densitized lapse slicings on evolutions of a wobbling black hole
• Energy Norms and the Stability of the Einstein Evolution Equations
• Stability properties of a formulation of Einstein's equations
• Stability of the puncture method with a generalized BSSN formulation
• Einstein boundary conditions for the Einstein equations in the conformal-traceless decomposition
• On the Hyperbolicity and Stability of $3+1$ Formulations of Metric $f(R)$ Gravity
• Improved fast-rotating black hole evolution simulations with modified Baumgarte-Shapiro-Shibata-Nakamura formulation
• Hamiltonian Relaxation
• Modifications for numerical stability of black hole evolution
• Aliasing Instabilities in the Numerical Evolution of the Einstein Field Equations