The initial value problem as it relates to numerical relativity
arXiv:1610.03805 · doi:10.1088/1361-6633/80/2/026901
Abstract
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the 3-metric and extrinsic curvature together with matter fields such as fluid velocity, energy density and rest mass density. There is a lot of freedom in choosing such initial data. This freedom corresponds to the physical state of the system at the initial time. At the same time the initial data have to satisfy the Hamiltonian and momentum constraint equations of General Relativity and can thus not be chosen completely freely. We discuss the conformal transverse traceless and conformal thin sandwich decompositions that are commonly used in the construction of constraint satisfying initial data. These decompositions allow us to specify certain free data that describe the physical nature of the system. The remaining metric fields are then determined by solving elliptic equations derived from the constraint equations. We describe initial data for single black holes and single neutron stars, and how we can use conformal decompositions to construct initial data for binaries made up of black holes or neutron stars. Orbiting binaries will emit gravitational radiation and thus lose energy. Since the emitted radiation tends to circularize the orbits over time, one can thus expect that the objects in a typical binary move on almost circular orbits with slowly shrinking radii. This leads us to the concept of quasi-equilibrium which essentially assumes that time derivatives are negligible in corotating coordinates, for binaries on almost circular orbits. We review how quasi-equilibrium assumptions can be used to make physically well motivated approximations that simplify the elliptic equations we have to solve.
64 pages, 5 figures, updated with version published in Reports on Progress in Physics
References in corpus (125)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- Advanced Virgo: a 2nd generation interferometric gravitational wave detector
- Evolution of Binary Black Hole Spacetimes
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Characterization of the LIGO detectors during their sixth science run
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- On the Numerical Integration of Einstein's Field Equations
- LIGO: The Laser Interferometer Gravitational-Wave Observatory
- Detector configuration of KAGRA - the Japanese cryogenic gravitational-wave detector
- The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
- Rotating Stars in Relativity
- Comparing Models of Rapidly Rotating Relativistic Stars Constructed by Two Numerical Methods
- A simple construction of initial data for multiple black holes
- GW150914: First results from the search for binary black hole coalescence with Advanced LIGO
- Low-frequency gravitational-wave science with eLISA/NGO
- Numerical Relativity Using a Generalized Harmonic Decomposition
- High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
- Dynamical Horizons and their Properties
- Calibration of Moving Puncture Simulations
- A single-domain spectral method for black hole puncture data
- Conformal ``thin sandwich'' data for the initial-value problem of general relativity
- Introduction to Isolated Horizons in Numerical Relativity
- Relativistic Numerical Method for Close Neutron Star Binaries
- Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests
- Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
- Generic Isolated Horizons and their Applications
- 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
- Initial Data for Numerical Relativity
- A multidomain spectral method for solving elliptic equations
- Extrinsic Curvature and the Einstein Constraints
- Gravitational wave astronomy
- Turduckening black holes: an analytical and computational study
- Reducing orbital eccentricity in binary black hole simulations
- Binary-black-hole initial data with nearly-extremal spins
- Excision boundary conditions for black hole initial data
- High-spin binary black hole mergers
- A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
- Binary black holes in circular orbits. II. Numerical methods and first results
- Binary black holes in circular orbits. I. A global spacetime approach
- Circular orbits and spin in black-hole initial data
- Merger of black hole-neutron star binaries in full general relativity
- Black hole-neutron star mergers: effects of the orientation of the black hole spin
- Simulations of non-equal mass black hole binaries with spectral methods
- Mergers of binary neutron stars with realistic spin
- Numerical models of irrotational binary neutron stars in general relativity
- Merger of black hole-neutron star binaries: nonspinning black hole case
- General Relativistic Models of Binary Neutron Stars in Quasiequilibrium
- Nonexistence of conformally flat slices of the Kerr spacetime
- Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions
- Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries
- Corotating and irrotational binary black holes in quasi-circular orbits
- On the black hole from merging binary neutron stars: how fast can it spin?
- Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral
- Eccentric binary neutron star mergers
- Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods
- Initial data for black hole-neutron star binaries: a flexible, high-accuracy spectral method
- Initial Data and Coordinates for Multiple Black Hole Systems
- Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models
- Eccentric black hole-neutron star mergers: effects of black hole spin and equation of state
- Effect of gravitational radiation reaction on nonequatorial orbits around a Kerr black hole
- A new numerical method for constructing quasi-equilibrium sequences of irrotational binary neutron stars in general relativity
- Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. III. Identical and different mass stars with gamma=2
- Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
- Filling the holes: Evolving excised binary black hole initial data with puncture techniques
- Eccentric Black Hole-Neutron Star Mergers
- New conformally flat initial data for spinning black holes
- Irrotational Binary Neutron Stars in Quasiequilibrium in General Relativity
- Highly accurate calculation of rotating neutron stars
- Excision without excision: the relativistic turducken
- Constructing quasi-equilibrium initial data for binary neutron stars with arbitrary spins
- Irrotational binary neutron stars in quasiequilibrium
- Binary black hole initial data for numerical general relativity based on post-Newtonian data
- Radiation-reaction-induced evolution of circular orbits of particles around Kerr Black Holes
- Constraint preserving boundary conditions for the Z4c formulation of general relativity
- A relativistic formalism for computation of irrotational binary stars in quasi equilibrium states
- Uniqueness and Non-uniqueness in the Einstein Constraints
- A new numerical method to construct binary neutron star initial data
- An approximate binary-black-hole metric
- Reducing orbital eccentricity in initial data of binary neutron stars
- Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions
- Relativistic black hole-neutron star binaries in quasiequilibrium: effects of the black hole excision boundary condition
- Quasiequilibrium black hole-neutron star binaries in general relativity
- Conformally curved binary black hole initial data including tidal deformations and outgoing radiation
- Various features of quasiequilibrium sequences of binary neutron stars in general relativity
- Binary black hole initial data from matched asymptotic expansions
- Initial data for binary neutron stars with arbitrary spins
- A multi-domain spectral method for scalar and vectorial Poisson equations with non-compact sources
- On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes
- Binary Neutron Stars with Arbitrary Spins in Numerical Relativity
- Conformal Thin-Sandwich Solver for Generic Initial Data
- Simulations of inspiraling and merging double neutron stars using the Spectral Einstein Code
- Solving the Initial Value Problem of two Black Holes
- Relativistic Hydrodynamics in Close Binary Systems: Analysis of Neutron-Star Collapse
- Binary black holes on a budget: Simulations using workstations
- Black hole puncture initial data with realistic gravitational wave content
- Binary neutron stars: Equilibrium models beyond spatial conformal flatness
- Non-conformally flat initial data for binary compact objects
- Binary Neutron-Star Systems: From the Newtonian Regime to the Last Stable Orbit
- Improvements to the construction of binary black hole initial data
- Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions
- Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems
- Quasiequilibrium sequences of black-hole--neutron-star binaries in general relativity
- A new code for equilibriums and quasiequilibrium initial data of compact objects
- Physics and Initial Data for Multiple Black Hole Spacetimes
- Asymptotic expansions of the Cotton-York tensor on slices of stationary spacetimes
- Stability under radiation reaction of circular equatorial orbits around Kerr black holes
- Eccentric mergers of black holes with spinning neutron stars
- Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium Formulation
- Initial data for binary neutron stars with adjustable eccentricity
- Multi-Domain Spectral Method for Initial Data of Arbitrary Binaries in General Relativity
- A Simple method to set up low eccentricity initial data for moving puncture simulations
- Inner boundary conditions for black hole Initial Data derived from Isolated Horizons
- Quasiequilibrium states of black hole-neutron star binaries in the moving-puncture framework
- Initial data for neutron star binaries with arbitrary spins
- Gauge conditions for binary black hole puncture data based on an approximate helical Killing vector
- Relativistic Models for Binary Neutron Stars with Arbitrary Spins
- Binary Neutron Stars in Quasi-equilibrium
- Numerical black hole initial data with low eccentricity based on post-Newtonian orbital parameters
- Models of helically symmetric binary systems
- Post-Newtonian Initial Data with Waves: Progress in Evolution
- Alternatives to standard puncture initial data for binary black hole evolution
- New code for equilibriums and quasiequilibrium initial data of compact objects. II. Convergence tests and comparisons of binary black hole initial data
- The Merger of Small and Large Black Holes
- Including realistic tidal deformations in binary black-hole initial data
- Initial data for high-compactness black hole-neutron star binaries
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- A new public code for initial data of unequal-mass, spinning compact-object binaries
- Numerical Relativity of Compact Binaries in the 21st Century
- Coalescence of black hole--neutron star binaries
- Magnetic tidal Love numbers clarified
- Constructing Binary Neutron Star Initial Data with High Spins, High Compactness, and High Mass-Ratios
- CTTK: A new method to solve the initial data constraints in numerical relativity
- Cooling binary neutron star remnants via nucleon-nucleon-axion bremsstrahlung
- Quasi-equilibrium configurations of binary systems of dark matter admixed neutron stars
- Hyperbolic Relaxation Method for Elliptic Equations
- The new discontinuous Galerkin methods based numerical relativity program Nmesh
- Gravitational waves and mass ejecta from binary neutron star mergers: Effect of the spin orientation
- High-accuracy simulations of highly spinning binary neutron star systems
- Conservation laws and evolution schemes in geodesic, hydrodynamic and magnetohydrodynamic flows
- Generic initial data for binary boson stars
- Elliptica: a new pseudo-spectral code for the construction of initial data
- Adaptive hp-Refinement for Spectral Elements in Numerical Relativity
- Boson star head-on collisions with constraint-violating and constraint-satisfying initial data
- Twist-free axisymmetric critical collapse of a complex scalar field
- NRPyElliptic: A Fast Hyperbolic Relaxation Elliptic Solver for Numerical Relativity, I: Conformally Flat, Binary Puncture Initial Data
- Parameter control for eccentric, precessing binary black hole simulations with SpEC
- Formulation Improvements for Critical Collapse Simulations
- Extending superposed harmonic initial data to higher spin
- Methods for relativistic self-gravitating fluids: From binary neutron stars to black hole-disks and magnetized rotating neutron stars
- Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild
- Twist and higher modes of a complex scalar field at the threshold of collapse
- Constraint-satisfying binary boson star initial data via XCFC