Stability of the puncture method with a generalized BSSN formulation

Abstract

The puncture method for dealing with black holes in the numerical simulation of vacuum spacetimes is remarkably successful when combined with the BSSN formulation of the Einstein equations. We examine a generalized class of formulations modeled along the lines of the Laguna-Shoemaker system, including BSSN as a special case. The formulation is a two parameter generalization of the choice of variables used in standard BSSN evolutions. Numerical stability of the standard finite difference methods is proven for the formulation in the linear regime around flat space, a special case of which is the numerical stability of BSSN. Numerical evolutions are presented and compared with a standard BSSN implementation. We find that a significant portion of the parameter space leads to stable evolutions and that standard BSSN is located near the edge of the stability region. Non-standard parameter choices typically result in smoother behaviour of the evolution variables close to the puncture and thus hold promise for improved accuracy in, e.g., long-term BH binary inspirals, and for overcoming (numerical) stability problems still encountered in some types of black-hole simulations, e.g., in $D\ge 6$ dimensions.

16 pages, 7 figures, 3 tables, matched to published version

References in corpus (20)

• Calibration of Moving Puncture Simulations
• Dynamical Chern-Simons Modified Gravity I: Spinning Black Holes in the Slow-Rotation Approximation
• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Binary black hole merger dynamics and waveforms
• Binary black-hole evolutions of excision and puncture data
• The high-energy collision of two black holes
• Geometry and Regularity of Moving Punctures
• Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions
• High-velocity collision of two black holes
• Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
• Wormholes and trumpets: the Schwarzschild spacetime for the moving-puncture generation
• Extra-Large Remnant Recoil Velocities and Spins from Near-Extremal-Bowen-York-Spin Black-Hole Binaries
• Numerical relativity for D dimensional space-times: head-on collisions of black holes and gravitational wave extraction
• Hyperbolicity of scalar-tensor theories of gravity
• Puncture Evolution of Schwarzschild Black Holes
• Status of black-hole-binary simulations for gravitational-wave detection
• Black holes in a box: towards the numerical evolution of black holes in AdS
• BSSN in Spherical Symmetry
• Comments on Bona-Masso type slicing conditions in long-term black hole evolutions
• Trumpet slices of the Schwarzschild-Tangherlini spacetime