Numerical Relativity and Compact Binaries

Abstract

Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the most promising sources of gravitational radiation for future detection by gravitational wave observatories. In this article we review numerical relativity approaches to modeling compact binaries. Starting with a brief introduction to the 3+1 decomposition of Einstein's equations, we discuss important components of numerical relativity, including the initial data problem, reformulations of Einstein's equations, coordinate conditions, and strategies for locating and handling black holes on numerical grids. We focus on those approaches which currently seem most relevant for the compact binary problem. We then outline how these methods are used to model binary neutron stars and black holes, and review the current status of inspiral and coalescence simulations.

122 pages, 19 figures; review article to appear in Physics Reports

References in corpus (107)

• On the Numerical Integration of Einstein's Field Equations
• Neutron Star Mass Measurements. I. Radio Pulsars
• A simple construction of initial data for multiple black holes
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Conformal ``thin sandwich'' data for the initial-value problem of general relativity
• Simulation of merging binary neutron stars in full general relativity: $\Gamma =2$ case
• Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests
• Measuring gravitational waves from binary black hole coalescences: II. the waves' information and its extraction, with and without templates
• Generic Isolated Horizons and their Applications
• Harmonic coordinate method for simulating generic singularities
• Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars
• The Transition from Inspiral to Plunge for a Compact Body in a Circular Equatorial Orbit Around a Massive, Spinning Black Hole
• The bar-mode instability in differentially rotating neutron stars: Simulations in full general relativity
• Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments
• Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
• Binary black holes in circular orbits. II. Numerical methods and first results
• Gravitational Waves from the Merger of Binary Neutron Stars in a Fully General Relativistic Simulation
• Fully general relativistic simulation of coalescing binary neutron stars: Preparatory tests
• Binary black holes in circular orbits. I. A global spacetime approach
• Black Hole Excision for Dynamic Black Holes
• Conformally Flat Smoothed Particle Hydrodynamics: Application to Neutron Star Mergers
• Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries
• Fixing Einstein's equations
• Simple excision of a black hole in 3+1 numerical relativity
• Three Dimensional Numerical General Relativistic Hydrodynamics I: Formulations, Methods, and Code Tests
• Numerical models of irrotational binary neutron stars in general relativity
• General Relativistic Models of Binary Neutron Stars in Quasiequilibrium
• Nonexistence of conformally flat slices of the Kerr spacetime
• Corotating and irrotational binary black holes in quasi-circular orbits
• A relativistic formalism to compute quasi-equilibrium configurations of non-synchronized neutron star binaries
• Thermodynamics of binary black holes and neutron stars
• Grazing Collisions of Black Holes via the Excision of Singularities
• Innermost circular orbit of binary black holes at the third post-Newtonian approximation
• First order hyperbolic formalism for Numerical Relativity
• Einstein's Equations with Asymptotically Stable Constraint Propagation
• Circular orbits of corotating binary black holes: comparison between analytical and numerical results
• Plunge waveforms from inspiralling binary black holes
• Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models
• Initial Data and Coordinates for Multiple Black Hole Systems
• A new numerical method for constructing quasi-equilibrium sequences of irrotational binary neutron stars in general relativity
• Stability and collapse of rapidly rotating, supramassive neutron stars: 3D simulations in general relativity
• Boundary conditions in linearized harmonic gravity
• The 3D Grazing Collision of Two Black Holes
• Hyperbolicity of the BSSN system of Einstein evolution equations
• Improved numerical stability of stationary black hole evolution calculations
• Quasi-circular Orbits for Spinning Binary Black Holes
• Constraint-preserving boundary conditions in numerical relativity
• Computing the merger of black-hole binaries: the IBBH problem
• Properties of general relativistic, irrotational binary neutron stars in close quasiequilibrium orbits : Polytropic equations of state
• Irrotational Binary Neutron Stars in Quasiequilibrium in General Relativity
• Comparing initial-data sets for binary black holes
• Irrotational binary neutron stars in quasiequilibrium
• A relativistic formalism for computation of irrotational binary stars in quasi equilibrium states
• Revised Relativistic Hydrodynamical Model for Neutron-Star Binaries
• Fully general relativistic simulation of merging binary clusters -- Spatial gauge condition --
• Pseudo-spectral apparent horizon finders: an efficient new algorithm
• Gravitational Collapse of Gravitational Waves in 3D Numerical Relativity
• Evolving the Bowen-York initial data for spinning black holes
• Test-beds and applications for apparent horizon finders in numerical relativity
• Solving the Initial Value Problem of two Black Holes
• Post-Newtonian Models of Binary Neutron Stars
• Binary Neutron-Star Systems: From the Newtonian Regime to the Last Stable Orbit
• The Stability of Relativistic Neutron Stars in Binary Orbit
• Well-posed forms of the 3+1 conformally-decomposed Einstein equations
• Possible explanation for star-crushing effect in binary neutron star simulations
• Cauchy boundaries in linearized gravitational theory
• Ill-posedness in the Einstein equations
• Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system
• Post-Newtonian SPH calculations of binary neutron star coalescence. III. Irrotational systems and gravitational wave spectra
• A Conformal Hyperbolic Formulation of the Einstein Equations
• Approximate Analytical Solutions to the Initial Data Problem of Black Hole Binary Systems
• Formulation for the internal motion of quasi-equilibrium configurations in general relativity
• Dilatonic Brane-World Black Holes, Gravity Localization and Newton Constant
• Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity
• Stability of coalescing binary stars against gravitational collapse: hydrodynamical simulations
• Computation of gravitational waves from inspiraling binary neutron stars in quasiequilibrium circular orbits : Formulation and calibration
• Symmetry-seeking spacetime coordinates
• Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test
• A cure for unstable numerical evolutions of single black holes: adjusting the standard ADM equations
• Improved initial data for black hole collisions
• Energy Norms and the Stability of the Einstein Evolution Equations
• Hyperbolic formulations and numerical relativity: Experiments using Ashtekar's connection variables
• Illustrating Stability Properties of Numerical Relativity in Electrodynamics
• Constraint propagation in the family of ADM systems
• Symmetric hyperbolic system in the Ashtekar formulation
• Locating Boosted Kerr and Schwarzschild Apparent Horizons
• Treating instabilities in a hyperbolic formulation of Einstein's equations
• Computing the Complete Gravitational Wavetrain from Relativistic Binary Inspiral
• Generic Tracking of Multiple Apparent Horizons with Level Flow
• Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of the Einstein equations
• Comparing the inspiral of irrotational and corotational binary neutron stars
• Quasi-stationary binary inspiral II: Radiation-balanced boundary conditions
• A new numerical scheme to compute 3D configurations of quasiequilibrium compact stars in general relativity -- Application to synchronously rotating binary star systems --
• Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime
• Stability properties of a formulation of Einstein's equations
• Radiative Falloff in Neutron Star Spacetimes
• A numerical testbed for singularity excision in moving black hole spacetimes
• Three-dimensional adaptive evolution of gravitational waves in numerical relativity
• Causal differencing of flux-conservative equations applied to black hole spacetimes
• Waveform propagation in black hole spacetimes: evaluating the quality of numerical solutions
• Gravitational Wavetrains in the Quasi-Equilibrium Approximation: A Model Problem in Scalar Gravitation
• A Linear-Nonlinear Formulation of Einstein Equations for the Two-Body Problem in General Relativity
• Incompressible fluid binary systems with internal flows -- models of close binary neutron star systems with spin
• Quasiequilibrium sequences of synchronously rotating binary neutron stars with constant rest masses in general relativity -- Another approach without using the conformally flat condition --
• Binary-Induced Gravitational Collapse: A Trivial Example
• Quasistationary binary inspiral. I. Einstein equations for the two Killing vector spacetime
• Binary-induced collapse of a compact, collisionless cluster

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• The Confrontation between General Relativity and Experiment
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• Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
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• A 3+1 perspective on null hypersurfaces and isolated horizons
• Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
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• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• Gravitational waves from neutron stars: Promises and challenges
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• 3D Collapse of Rotating Stellar Iron Cores in General Relativity including Deleptonization and a Nuclear Equation of State
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• A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
• Numerical Methods for Finding Stationary Gravitational Solutions
• A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation
• High accuracy binary black hole simulations with an extended wave zone
• Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
• The self-consistent gravitational self-force
• Black holes and fundamental fields in Numerical Relativity: initial data construction and evolution of bound states
• Toward standard testbeds for numerical relativity
• Gravitomagnetic resonant excitation of Rossby modes in coalescing neutron star binaries
• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• Effect of Differential Rotation on the Maximum Mass of Neutron Stars: Realistic Nuclear Equations of State
• Mapping Ricci-based theories of gravity into general relativity
• Torus Formation in Neutron Star Mergers and Well-Localized Short Gamma-Ray Bursts
• Mode coupling in the nonlinear response of black holes
• The Dynamical Evolution of Black Hole-Neutron Star Binaries in General Relativity: Simulations of Tidal Disruption
• Constraining Sub-Parsec Binary Supermassive Black Holes in Quasars with Multi-Epoch Spectroscopy. III. Candidates from Continued Radial Velocity Tests
• Cosmological apparent and trapping horizons
• Gravito-electromagnetic analogies
• Golden Binary Gravitational-Wave Sources: Robust Probes of Strong-Field Gravity
• Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics
• Foliation dependence of black hole apparent horizons in spherical symmetry
• Summation by parts and dissipation for domains with excised regions
• 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
• Foundations of Relational Particle Dynamics
• Various features of quasiequilibrium sequences of binary neutron stars in general relativity
• Binary black hole initial data from matched asymptotic expansions
• Black hole-neutron star binaries in general relativity: effects of neutron star spin
• Gravitational waves from merging compact binaries
• Impact of the nuclear equation of state on the last orbits of binary neutron stars
• Black hole merger simulations in wave dark matter environments
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Dynamical Determination of the Innermost Stable Circular Orbit of Binary Neutron Stars
• Binary neutron stars: Equilibrium models beyond spatial conformal flatness
• Two-step greedy algorithm for reduced order quadratures
• Strategies for observing extreme mass ratio inspirals
• Horizon energy and angular momentum from a Hamiltonian perspective
• Quasiequilibrium sequences of black-hole--neutron-star binaries in general relativity
• A Reinvestigation of Moving Punctured Black Holes with a New Code
• The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach
• Merger of white dwarf-neutron star binaries: Prelude to hydrodynamic simulations in general relativity
• Black brane entropy and hydrodynamics: the boost-invariant case
• New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
• Relativistic hydrodynamics in the presence of puncture black holes
• Head-on collisions of binary white dwarf--neutron stars: Simulations in full general relativity
• Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium Formulation
• Multi-Domain Spectral Method for Initial Data of Arbitrary Binaries in General Relativity
• Are quantization rules for horizon areas universal?
• Relativistic Models for Binary Neutron Stars with Arbitrary Spins
• Triangleland. I. Classical dynamics with exchange of relative angular momentum
• Einstein boundary conditions for the 3+1 Einstein equations
• Quasi-equilibrium Binary Black Hole Initial Data for Dynamical Evolutions
• Binary Neutron Stars in Quasi-equilibrium
• Are neutron stars crushed? Gravitomagnetic tidal fields as a mechanism for binary-induced collapse
• Gravitational Waves from Extragalactic Inspiraling Binaries: Selection Effects and Expected Detection Rates
• Last orbits of binary strange quark stars
• A new spectral apparent horizon finder for 3D numerical relativity
• Approximate initial data for binary black holes
• K-dynamics: well-posed 1+1 evolutions in K-essence
• Full 3D Numerical Relativity Simulations of Neutron Star -- Boson Star Collisions with BAM
• Generalised Boundary Terms for Higher Derivative Theories of Gravity
• Finding apparent horizons and other two-surfaces of constant expansion
• Horizon thermodynamics and spacetime mappings
• General-relativistic treatment of tidal $g$-mode resonances in coalescing binaries of neutron stars. II. As triggers for precursor flares of short gamma-ray bursts
• Quasi-equilibrium models for triaxially deformed rotating compact stars
• Can a combination of the conformal thin-sandwich and puncture methods yield binary black hole solutions in quasi-equilibrium?
• Accelerated expansion from cosmological holography
• Trumpet-puncture initial data for black holes
• The discrete energy method in numerical relativity: Towards long-term stability
• Rotating star initial data for a constrained scheme in numerical relativity
• Towards a wave--extraction method for numerical relativity: III. Analytical examples for the Beetle--Burko radiation scalar
• The Gravitational Wave Signature of Core-Collapse Supernovae
• Alternatives to standard puncture initial data for binary black hole evolution
• A formalism for the construction of binary neutron stars with arbitrary circulation
• Dynamical apparent horizons in inhomogeneous Brans-Dicke universes
• Numerical computation of constant mean curvature surfaces using finite elements
• An axion-like scalar field environment effect on binary black hole merger
• Constraint propagation equations of the 3+1 decomposition of f(R) gravity
• The periodic standing-wave approximation: nonlinear scalar fields, adapted coordinates, and the eigenspectral method
• The final phase of inspiral of neutron stars: realistic equations of state
• Generalized harmonic formulation in spherical symmetry
• On The Dark Side of Quasar Evolution
• Excision boundary conditions for the conformal metric
• Binary black hole evolutions of approximate puncture initial data
• Excising a boosted rotating black hole with overlapping grids
• Frankenstein's Glue: Transition functions for approximate solutions
• Parameter control for eccentric, precessing binary black hole simulations with SpEC
• Lecture Notes: Numerical Relativity in higher dimensional spacetimes
• Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity
• Conformal thin-sandwich puncture initial data for boosted black holes
• Numerical performance of the parabolized ADM (PADM) formulation of General Relativity
• A Numerical Study of Boson Star Binaries
• Simulating gravitational waves passing through the spacetime of a black hole
• High-Precision Numerical Simulations of Rotating Black Holes Accelerated by CUDA
• Motion of small bodies in general relativity: foundations and implementations of the self-force
• Constraint propagation in N+1-dimensional space-time
• A study of different horizons in inhomogeneous LTB cosmological model
• Equilibrium initial data for moving puncture simulations: The stationary 1+log slicing
• Towards a wave-extraction method for numerical relativity. V. Extracting the Weyl scalars in the quasi-Kinnersley tetrad from spatial data
• Gravitational-wave searches in the era of Advanced LIGO and Virgo
• Two physical characteristics of numerical apparent horizons
• Well-posed constrained evolution of 3+1 formulations of General Relativity
• A Black-Hole Excision Scheme for General Relativistic Core-Collapse Supernova Simulations
• Why Solve the Hamiltonian Constraint in Numerical Relativity?
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• Quantum Cosmological Relational Model of Shape and Scale in 1-d
• Evolving black hole horizons in General Relativity and alternative gravity
• Discrete differential forms for cosmological space-times
• First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
• Shells around black holes: the effect of freely specifiable quantities in Einstein's constraint equations
• Black Hole Formation and Growth: Simulations in General Relativity
• Numerical solutions for the $f(R)$-Klein-Gordon system
• On the recovery of geometrodynamics from two different sets of first principles
• Conditional Autoencoder for Generating Binary Neutron Star Waveforms with Tidal and Precession Effects
• Perturbative Analytical Construction of Bowen-York Initial Data for Binary Black Holes up to Third Order in Spin and Linear Momentum
• Embedding black holes and other inhomogeneities in the universe in various theories of gravity: a short review