A symmetry-breaking mechanism for the Z4 general-covariant evolution system
arXiv:gr-qc/0307067 · doi:10.1103/PhysRevD.69.064036
Abstract
The general-covariant Z4 formalism is further analyzed. The gauge conditions are generalized with a view to Numerical Relativity applications and the conditions for obtaining strongly hyperbolic evolution systems are given both at the first and the second order levels. A symmetry-breaking mechanism is proposed that allows one, when applied in a partial way, to recover previously proposed strongly hyperbolic formalisms, like the BSSN and the Bona-Massó ones. When applied in its full form, the symmetry breaking mechanism allows one to recover the full five-parameter family of first order KST systems. Numerical codes based in the proposed formalisms are tested. A robust stability test is provided by evolving random noise data around Minkowski space-time. A strong field test is provided by the collapse of a periodic background of plane gravitational waves, as described by the Gowdy metric.
arXiv commentfigures added, text changed, accepted in PRD
References in corpus (13)
- On the Numerical Integration of Einstein's Field Equations
- New Formalism for Numerical Relativity
- General-covariant evolution formalism for Numerical Relativity
- Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
- Fixing Einstein's equations
- On the Newtonian Limit of General Relativity
- Grazing Collisions of Black Holes via the Excision of Singularities
- First-order symmetric-hyperbolic Einstein equations with arbitrary fixed gauge
- Einstein's Equations with Asymptotically Stable Constraint Propagation
- Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing
- A 3+1 covariant suite of Numerical Relativity Evolution Systems
- Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein's equations
- The constraints as evolution equations for numerical relativity
Cited by in corpus (54)
- Binary neutron-star mergers: a review of Einstein's richest laboratory
- Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
- Constraint damping in the Z4 formulation and harmonic gauge
- Conformal and covariant formulation of the Z4 system with constraint-violation damping
- Compact binary evolutions with the Z4c formulation
- Gravitational Wave Signatures of Highly Compact Boson Star Binaries
- Extraction of Gravitational Waves in Numerical Relativity
- Multi-state Boson Stars
- On the final fate of compact boson star mergers
- On the gravitational radiation from the collapse of neutron stars to rotating black holes
- Nonlinear interactions between black holes and Proca fields
- Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars
- Constraint damping for the Z4c formulation of general relativity
- Numerical evolutions of a black hole-neutron star system in full General Relativity: I. Head-on collision
- Exploring New Physics Frontiers Through Numerical Relativity
- Constraint preserving boundary conditions for the Z4c formulation of general relativity
- Conformal and covariant Z4 formulation of the Einstein equations: strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes
- Gravitational wave signatures of dark matter cores in binary neutron star mergers by using numerical simulations
- Dynamical ejecta and nucleosynthetic yields from eccentric binary neutron-star mergers
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
- On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations
- Constraint-preserving boundary conditions in the Z4 Numerical Relativity formalism
- Numerical stability of the Z4c formulation of general relativity
- Spherical symmetry as a test case for unconstrained hyperboloidal evolution
- GRMHD large eddy simulations with gradient subgrid-scale model
- Dynamical shift conditions for the Z4 and BSSN hyperbolic formalisms
- A strongly hyperbolic and regular reduction of Einstein's equations for axisymmetric spacetimes
- Numerical stability for finite difference approximations of Einstein's equations
- Gravitational Collapse in Cubic Horndeski Theories
- Towards a gauge-polyvalent Numerical Relativity code
- Regularization of spherical and axisymmetric evolution codes in numerical relativity
- Introduction to Numerical Relativity
- Finite differencing second order systems describing black hole spacetimes
- Efficient implementation of finite volume methods in Numerical Relativity
- Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations
- Action principle for Numerical Relativity evolution systems
- Large Eddy Simulations of Magnetized Mergers of Black Holes and Neutron Stars
- Boundary Conditions for the Gravitational Field
- Constraint-preserving boundary conditions in the 3+1 first-order approach
- Lecture Notes: Numerical Relativity in higher dimensional spacetimes
- Numerical stability of the AA evolution system compared to the ADM and BSSN systems
- Disembodied boundary data for Einstein's equations
- The initial boundary value problem for free-evolution formulations of General Relativity
- Hamiltonian Relaxation
- Well-balanced high order finite difference WENO schemes for a first-order Z4 formulation of the Einstein field equations
- Action Principle for the Generalized Harmonic Formulation of General Relativity
- Constraint Propagation of -adjusted Formulation II --- Another Recipe for Robust Baumgarte-Shapiro-Shibata-Nakamura Evolution System ---
- Hypergraph Discretization of the Cauchy Problem in General Relativity via Wolfram Model Evolution
- High-order discontinuous Galerkin schemes with subcell finite volume limiter and adaptive mesh refinement for a monolithic first-order BSSNOK formulation of the Einstein-Euler equations
- Gravitational systems in asymptotically anti-de Sitter space-times
- ExaGRyPE: Numerical General Relativity Solvers Based upon the Hyperbolic PDEs Solver Engine ExaHyPE
- Free Hyperboloidal Evolution of the Einstein-Maxwell-Klein-Gordon System
- Dynamical Chameleon Neutron Stars: stability, radial oscillations and scalar radiation in spherical symmetry
- Some mathematical problems in numerical relativity