Stable long-term evolution in numerical relativity
arXiv:2501.01055 · doi:10.1103/PhysRevD.111.084018
Abstract
We report on the potential occurrence of a numerical instability in the long-time simulation of black holes using the Baumgarte-Shapiro-Shibata-Nakamura formulation of numerical relativity, even in the simple set-up of a Schwarzschild black hole. Through extensive numerical experiments, we identify that this "late-time instability" arises from accumulated violations of the momentum constraint. To address this issue, we propose two modified versions of the so-called conformal covariant Z4 scheme, designed to propagate momentum constraint violations without damping. Our results demonstrate that these alternative formulations, which we refer to as CCZ4' and CCZ3, effectively resolve the late-time numerical instability not only in Schwarzschild spacetimes but also in black hole spacetimes with matter fields. Notably, by preventing damping of the momentum constraint violation, the Hamiltonian constraint damping can be significantly increased, which plays a crucial role in stabilizing long-term evolution in our proposed schemes.
19+5 pages; v2: matches published version
References in corpus (34)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
- String Axiverse
- First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
- Evolution of Binary Black Hole Spacetimes
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- Instability of the massive Klein-Gordon field on the Kerr spacetime
- The black hole bomb and superradiant instabilities
- Spontaneous scalarisation of charged black holes
- Constraint damping in the Z4 formulation and harmonic gauge
- Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
- Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes
- Conformal and covariant formulation of the Z4 system with constraint-violation damping
- Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
- Compact binary evolutions with the Z4c formulation
- Superradiant instabilities of rotating black holes in the time domain
- Explosion and final state of an unstable Reissner-Nordstrom black hole
- Covariant formulations of BSSN and the standard gauge
- Exotic Compact Objects and the Fate of the Light-Ring Instability
- Black Hole Dynamics in Einstein-Maxwell-Dilaton Theory
- Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars
- SENR/NRPy+: Numerical Relativity in Singular Curvilinear Coordinate Systems
- Time Step Size Limitation Introduced by the BSSN Gamma Driver
- Constraint preserving boundary conditions for the Z4c formulation of general relativity
- The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes
- Numerical stability of the Z4c formulation of general relativity
- Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit
- Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry
- Probing the puncture for black hole simulations
- Improved Moving-Puncture Techniques for Compact Binary Simulations
- Relativistic radiation hydrodynamics in a reference-metric formulation
- Black hole accretion of scalar clouds with spontaneous symmetry breaking
- On the stability of covariant BSSN formulation