Height-function-based 4D reference metrics for hyperboloidal evolution
arXiv:2408.08952 · doi:10.1007/s10714-024-03323-8
Abstract
Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the formally-singular conformally compactified Einstein equations in spherical symmetry. One way to construct gauge conditions suitable for this approach relies on building the gauge source functions from a time-independent background spacetime metric. This background reference metric is set using the height function approach to provide the correct asymptotics of hyperboloidal slices of Minkowski spacetime. The present objective is to study the effect of different choices of height function on hyperboloidal evolutions via the reference metrics used in the gauge conditions. A total of 10 reference metrics for Minkowski are explored, identifying some of their desired features. They include 3 hyperboloidal layer constructions, evolved with the non-linear Einstein equations for the first time. Focus is put on long-term numerical stability of the evolutions, including small initial gauge perturbations. The results will be relevant for future (puncture-type) hyperboloidal evolutions, 3D simulations and the development of coinciding Cauchy and hyperboloidal data, among other applications.
arXiv comment19 pages, 14 figures; matches published version, part of topical collection "Hyperboloidal foliations in the era of gravitational-wave astronomy: from mathematical relativity to astrophysics''
References in corpus (47)
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- On the Numerical Integration of Einstein's Field Equations
- Gauge conditions for long-term numerical black hole evolutions without excision
- A simple construction of initial data for multiple black holes
- New Formalism for Numerical Relativity
- 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
- A new approach to static numerical relativity, and its application to Kaluza-Klein black holes
- General-covariant evolution formalism for Numerical Relativity
- A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
- Hyperboloidal foliations and scri-fixing
- Covariant formulations of BSSN and the standard gauge
- A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime
- Numerical Relativity in Spherical Polar Coordinates: Evolution Calculations with the BSSN Formulation
- Constraint damping for the Z4c formulation of general relativity
- Null infinity waveforms from extreme-mass-ratio inspirals in Kerr spacetime
- Binary black hole coalescence in the large-mass-ratio limit: the hyperboloidal layer method and waveforms at null infinity
- The appearance of coordinate shocks in hyperbolic formalisms of General Realtivity
- Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform
- Hyperboloidal layers for hyperbolic equations on unbounded domains
- BSSN equations in spherical coordinates without regularization: vacuum and non-vacuum spherically symmetric spacetimes
- Hyperboloidal evolution with the Einstein equations
- Late time behaviour of the maximal slicing of the Schwarzschild black hole
- Numerical solution of the 2+1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late-time decays
- Horizon-absorption effects in coalescing black-hole binaries: An effective-one-body study of the non-spinning case
- Implementation of standard testbeds for numerical relativity
- Constant mean curvature slices in the extended Schwarzschild solution and collapse of the lapse: Part I
- General relativistic hydrodynamics in curvilinear coordinates
- Lumpy AdS S Black Holes and Black Belts
- Numerical stability of the Z4c formulation of general relativity
- Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
- Spherical symmetry as a test case for unconstrained hyperboloidal evolution
- BSSN in Spherical Symmetry
- Numerical relativity with the conformal field equations
- Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation tests
- Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry
- Spherical symmetry as a test case for unconstrained hyperboloidal evolution II: gauge conditions
- Constant Crunch Coordinates for Black Hole Simulations
- The Hyperboloidal Numerical Evolution of a Good-Bad-Ugly Wave Equation
- Comments on Bona-Masso type slicing conditions in long-term black hole evolutions
- Unconstrained hyperboloidal evolution of black holes in spherical symmetry with GBSSN and Z4c
- Shock-avoiding slicing conditions: tests and calibrations
- Summation by Parts and Truncation Error Matching on Hyperboloidal Slices
- Spherically symmetric black hole spacetimes on hyperboloidal slices
- Conformal diagrams for stationary and dynamical strong-field hyperboloidal slices
- Dynamical perturbations of black-hole punctures: effects of slicing conditions
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- Hyperboloidal Approach to Quasinormal Modes
- Merging black holes with Cauchy-characteristic matching: Computation of late-time tails
- Cosmology using numerical relativity
- Free Hyperboloidal Evolution of the Einstein-Maxwell-Klein-Gordon System
- Charged Scalar Field at Future Null Infinity via Nonlinear Hyperboloidal Evolution
- A numerical approach to particle creation in accelerating toy models
- Topical Collection-Hyperboloidal Foliations in the Era of Gravitational-Wave Astronomy: From Mathematical Relativity to Astrophysics
- Hyperboloidal neutron star and black hole initial data in spherical symmetry