We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral methods, while the fluids are evolved on another grid using shock-capturing finite difference or finite volume techniques. We show that the code accurately evolves equilibrium stars and accretion flows. Then we simulate an equal-mass nonspinning black hole-neutron star binary, evolving through the final four orbits of inspiral, through the merger, to the final stationary black hole. The gravitational waveform can be reliably extracted from the simulation.
With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving hyperbolic equations. The calculations are carried out within the framework of conformally compactified space-times. In our formulation, the equation becomes singular at null infinity and yields regular boundary conditions there. In this manner it becomes possible to avoid "artificial" conditions at some numerical outer boundary at a finite distance. We obtain high…
The prime candidate of LIGO/VIRGO sources of gravitational waves is the spiral in of black holes and neutron stars in compact binaries. While the early stages of the evolution of compact binaries is computable from post-Newtonian calculations, prediction of their late stages requires large scale numerical simulation. A fully covariant and strictly hyperbolic formulation for numerical relativity is described, and illustrated in a one-dimensional computation of a Gowdy-wave on the three-torus. This formulation allows foliations in full generality, in particular it poses no restriction on the lap…
We present a new pseudospectral code, bamps, for numerical relativity written with the evolution of collapsing gravitational waves in mind. We employ the first order generalized harmonic gauge formulation. The relevant theory is reviewed and the numerical method is critically examined and specialized for the task at hand. In particular we investigate formulation parameters, gauge and constraint preserving boundary conditions well-suited to non-vanishing gauge source functions. Different types of axisymmetric twist-free moment of time symmetry gravitational wave initial data are discussed. A tr…
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 …
I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical parameter estimation in modern interferometric gravitational wave detectors. Using a post-Newtonian point particle model for the pre-merger phase of the binary inspiral, I calculate the maximum allowable errors for the mass and relative velocity and positions of the binary during numerical simulations of the binary inspiral. These maximum allowable errors are compa…
We present a new numerical method for the construction of quasiequilibrium models of black hole-neutron star binaries. We solve the constraint equations of general relativity, decomposed in the conformal thin-sandwich formalism, together with the Euler equation for the neutron star matter. We take the system to be stationary in a corotating frame and thereby assume the presence of a helical Killing vector. We solve these coupled equations in the background metric of a Kerr-Schild black hole, which accounts for the neutron star's black hole companion. In this paper we adopt a polytropic equatio…
We construct quasiequilibrium sequences of black hole-neutron star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition. We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics, and account for the black hole by imposing equilibrium boundary conditions on the surface of an excised sphere (the apparent horizon). In this paper we focus on irrotational configurations, meaning that both the neutron star and the black hole are approximately nonspinning in an inerti…
Gravitational-wave data analysis requires a detailed understanding of the highly relativistic, late stages of inspiral of neutron-star and black-hole binaries. A promising method to compute the late inspiral and its emitted waves is numerical relativity in co-rotating coordinates. The coordinates must be kept co-rotating via an appropriate choice of numerical relativity's lapse and shift functions. This article proposes a model problem for testing the ability of various lapse and shift prescriptions to keep the coordinates co-rotating.
We construct quasiequilibrium sequences of black hole-neutron star binaries in general relativity. We solve Einstein's constraint equations in the conformal thin-sandwich formalism, subject to black hole boundary conditions imposed on the surface of an excised sphere, together with the relativistic equations of hydrostatic equilibrium. In contrast to our previous calculations we adopt a flat spatial background geometry and do not assume extreme mass ratios. We adopt a Gamma=2 polytropic equation of state and focus on irrotational neutron star configurations as well as approximately nonspinning…
We present our latest results for simulation for merger of black hole (BH)-neutron star (NS) binaries in full general relativity which is performed preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the $Γ$-law equation of state with $Γ=2$ and corotating velocity field as a first step. The mass of the BH is chosen to be $\approx 3.2 M_{\odot}$ or $4.0M_{\odot}$, and the rest-mass of the NS $\approx 1.4 M_{\odot}$ with relatively large radius of the NS $\approx 13$--14 km. The NS is tidally disrupted near the innermost stable …
We present new sequences of general relativistic, quasiequilibrium black hole-neutron star binaries. We solve for the gravitational field in the conformal thin-sandwich decomposition of Einstein's field equations, coupled to the equations of relativistic hydrostatic equilibrium for a perfect fluid. We account for the black hole by solving these equations in the background metric of a Schwarzschild black hole whose mass is much larger than that of the neutron star. The background metric is treated in Kerr-Schild as well as isotropic coordinates. For the neutron star, we assume a polytropic equa…
The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test. All of these tests are found …
We present a new phenomenological gravitational waveform model for the inspiral and coalescence of non-precessing spinning black hole binaries. Our approach is based on a frequency domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near th…
We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of binaries containing black holes and neutron stars, as well as simulations of black-hole formation through failed supernovae and high-mass neutron star--neutron star mergers. Modeling such events requires numerical integration of the field equations of general relativity in three spatial dimensions, coupled, in the case of neutron-star containing binaries, wit…
Observations of the inspiral of massive binary black holes (BBH) in the Laser Interferometer Space Antenna (LISA) and stellar mass binary black holes in the European Gravitational-Wave Observatory (EGO) offer an unique opportunity to test the non-linear structure of general relativity. For a binary composed of two non-spinning black holes, the non-linear general relativistic effects depend only on the masses of the constituents. In a recent letter, we explored the possibility of a test to determine all the post-Newtonian coefficients in the gravitational wave-phasing. However, mutual covarianc…
We study the general relativistic periastron advance in spinning black hole binaries on quasi-circular orbits, with spins aligned or anti-aligned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result, and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the perias…
We compare results from numerical simulations of spinning binaries in the "orbital hangup" case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants TaylorT1, T4 and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches $Mω= 0.1$, the accumulated phase disagreement between NR and 2.5PN results is less than three radians, and is less than 2.5 radians when using 3.5PN results. The amplitude disagreement between NR and restricted PN results increases with the black holes' spin, from about 6% in the equal…
We consider the observation of stellar-mass black holes binaries with the Laser Interferometer Space Antenna (LISA). Preliminary results based on Fisher information matrix analyses have suggested that gravitational waves from those sources could be very sensitive to possible deviations from the theory of general relativity and from the strong equivalence principle during the low-frequency binary inspiral. We perform a full Markov Chain Monte Carlo Bayesian analysis to quantify the sensitivity of these signals to two phenomenological modifications of general relativity, namely a putative gravit…
We study black-hole binaries in the intermediate-mass-ratio regime 0.01 < q < 0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO/VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully-nonlinear numerical simulations.
We present a multi-domain spectral method to compute initial data of binary systems in General Relativity. By utilizing adapted conformal coordinates, the vacuum region exterior to the gravitational sources is divided up into two subdomains within which the spectral expansion of the field quantities is carried out. If a component of the binary is a neutron star, a further subdomain covering the star's interior is added. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes, binary neutron stars or mixed binaries. In particular, it is possible t…
Mergers of binary neutron stars and black hole-neutron star binaries are one of the most promising sources for the ground-based gravitational-wave (GW) detectors and also a high-energy astrophysical phenomenon as illustrated by the observations of gravitational waves and electromagnetic (EM) waves in the event of GW170817. Mergers of these neutron-star binaries are also the most promising site for r-process nucleosynthesis. Numerical simulation in full general relativity (numerical relativity) is a unique approach to the theoretical prediction of the merger process, GWs emitted, mass ejection …
Using accurate numerical relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1 and 3:1 we compute the gauge invariant relation between the (reduced) binding energy $E$ and the (reduced) angular momentum $j$ of the system. We show that the relation $E(j)$ is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity $E^{\rm NR} (j)$ curve with the predictions of several analytic approximation schemes, we find that, while the usual, non-resummed post-Newtonian-expanded $E^{\rm PN} (j)$ relat…
We calculate the first dynamical evolutions of merging black hole-neutron star binaries that construct the combined black hole-neutron star spacetime in a general relativistic framework. We treat the metric in the conformal flatness approximation, and assume that the black hole mass is sufficiently large compared to that of the neutron star so that the black hole remains fixed in space. Using a spheroidal spectral methods solver, we solve the resulting field equations for a neutron star orbiting a Schwarzschild black hole. The matter is evolved using a relativistic, Lagrangian, smoothed partic…
We investigate the production of gravitational waves during the inspiral of compact binaries close to their merger in the context of a conformal gravity model. The model incorporates five massive polarization degrees of freedom, besides the two massless gravitational wave polarizations of general relativity. For small graviton mass, we find that the amplitude of the gravitational waves is strongly suppressed as compared to general relativity and decreases as coalescence is approached, which contradicts the observational fact. We conclude that this model with small graviton mass, including a re…
Inspiraling compact binaries are expected to be the strongest sources of gravitational waves for VIRGO, LIGO and other laser interferometers. We present the first computations of quasi-equilibrium sequences of compact binaries containing two strange quark stars (which are currently considered as a possible alternative to neutron stars). We study a precoalescing stage in the conformal flatness approximation of general relativity using a multidomain spectral method. A hydrodynamical treatment is performed under the assumption that the flow is irrotational.
We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the effect of spin and minidisks on the accretion rate and Poynting luminosity variability. We report on the structure of the minidisks and periodicities in the mass of the minidisks, mass accretion rates, and Poynting luminosity. The accretion rate exhibits a quasi-periodic behavior related to the orbital frequency of the binary in all systems that we study, but the amplitude of this modulation is dependent on the existence of persistent minidisks. In particular, syste…
Models of gravitational waveforms from coalescing black-hole binaries play a crucial role in the efforts to detect and interpret the signatures of those binaries in the data of large-scale interferometers. Here we summarize recent models that combine information both from analytical approximations and numerical relativity. We briefly lay out and compare the strategies employed to build such complete models and we recapitulate the errors associated with various aspects of the modelling process.
We review the current status of attempts to numerically model the merger of neutron star-neutron star (NSNS) and black hole-neutron star (BHNS) binary systems, and we describe the understanding of such events that is emerging from these calculations. To accurately model the physics of NSNS and BHNS mergers is a difficult task. It requires solving Einstein's equations for dynamic spacetimes containing black holes. It also requires evolving the hot, supernuclear-density neutron star matter together with the magnetic and radiation fields that can influence the post-merger dynamics. Older studies …
The coalescences of stellar-mass black-hole binaries through their inspiral, merger, and ringdown are among the most promising sources for ground-based gravitational-wave (GW) detectors. If a GW signal is observed with sufficient signal-to-noise ratio, the masses and spins of the black holes can be estimated from just the inspiral part of the signal. Using these estimates of the initial parameters of the binary, the mass and spin of the final black hole can be uniquely predicted making use of general-relativistic numerical simulations. In addition, the mass and spin of the final black hole can…
We improve the effective-one-body (EOB) description of nonspinning coalescing black hole binaries by incorporating several recent analytical advances, notably: (i) logarithmic contributions to the conservative dynamics; (ii) resummed horizon-absorption contribution to the orbital angular momentum loss; and (iii) a specific radial component of the radiation reaction force implied by consistency with the azimuthal one. We then complete this analytically improved EOB model by comparing it to accurate numerical relativity (NR) simulations performed by the Caltech-Cornell-CITA group for mass ratios…
General relativity (GR) has been extensively tested in the solar system and in binary pulsars, but never in the strong-field, dynamical regime. Soon, gravitational-wave (GW) detectors like Advanced LIGO and eLISA will be able to probe this regime by measuring GWs from inspiraling and merging compact binaries. One particularly interesting alternative to GR is scalar-tensor gravity. We present progress in the calculation of second post-Newtonian (2PN) gravitational waveforms for inspiraling compact binaries in a general class of scalar-tensor theories. The waveforms are constructed using a stand…
The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory, numerical relativity, and the effective-one-body formalism. We review two recent comparisons of the predictions from these various techniques. Both comparisons rely on the calculation of a coordinate invariant relation, in the case of non-spinning binary black holes on quasi-circular orbits. All methods are shown to agree very well in their common domain of v…
Although General Relativity (GR) has been tested extensively in the weak gravity regime, similar tests in the strong gravity regime are still missing. In this paper we explore the possibility to use X-ray spectropolarimetric observations of black holes in X-ray binaries to distinguish between the Kerr metric and the phenomenological metrics introduced by Johannsen and Psaltis (2011) (which are not vacuum solutions of Einstein's equation) and thus to test the no-hair theorem of GR. To this end, we have developed a numerical code that calculates the radial brightness profiles of accretion disks …
The second generation of gravitational-wave detectors is scheduled to start operations in 2015. Gravitational-wave signatures of compact binary coalescences could be used to accurately test the strong-field dynamical predictions of general relativity. Computationally expensive data analysis pipelines, including TIGER, have been developed to carry out such tests. As a means to cheaply assess whether a particular deviation from general relativity can be detected, Cornish et al. and Vallisneri recently proposed an approximate scheme to compute the Bayes factor between a general-relativity gravita…
Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational waveforms can only be calculated through numerical simulations of Einstein's equations of general relativity. For many years, numerical relativists att…
Testing gravitational theories by binary pulsars nowadays becomes a key issue. For the general screened modified gravity (SMG), the post-Keplerian parameters in the neutron star (NS) - white dwarf (WD) binaries differ from those of general relativity (GR), and the differences are quantified by the scalar charge $ε_{\scriptscriptstyle\rm WD}$ of WD. After deriving the constraints on $ε_{\scriptscriptstyle\rm WD}$ from four different NS-WD binaries, we find that $ε_{\scriptscriptstyle\rm WD}$ is different from zero at the 2$σ$ level in all the cases studied, and there exists an inverse correlati…
We present an analytical formalism, within the Effective-One-Body framework, which predicts gravitational-wave signals from inspiralling and coalescing black-hole binaries that agree, within numerical errors, with the results of the currently most accurate numerical relativity simulations for several different mass ratios. In the equal-mass case, the gravitational wave energy flux predicted by our formalism agrees, within numerical errors, with the most accurate numerical-relativity energy flux. We think that our formalism opens a realistic possibility of constructing a sufficiently accurate, …
White dwarf-neutron star binaries generate detectable gravitational radiation. We construct Newtonian equilibrium models of corotational white dwarf-neutron star (WDNS) binaries in circular orbit and find that these models terminate at the Roche limit. At this point the binary will undergo either stable mass transfer (SMT) and evolve on a secular time scale, or unstable mass transfer (UMT), which results in the tidal disruption of the WD. The path a given binary will follow depends primarily on its mass ratio. We analyze the fate of known WDNS binaries and use population synthesis results to e…
Binary black holes with spins that are aligned with the orbital angular momentum do not precess. However, post-Newtonian calculations predict that "up-down" binaries, in which the spin of the heavier (lighter) black hole is aligned (antialigned) with the orbital angular momentum, are unstable when the spins are slightly perturbed from perfect alignment. This instability provides a possible mechanism for the formation of precessing binaries in environments where sources are preferentially formed with (anti) aligned spins. In this paper, we present the first full numerical relativity simulations…
We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasi-circular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron advance recently computed in accurate numerical-relativity simulations and find remarkable agreement for a wide range of spins and mass ratios. These results do not use any numerical-relativity calibration of the effective-one-body model, and stem from two key ingredients in the effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of spinnin…
We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100:1. Our technique for evolving such extreme mass ratios is based on the moving puncture approach with a new gauge condition and an optimal choice of the mesh refinement (plus large computational resources). We achieve a convergent set of results for simulations starting with a small nonspinning black hole just outside the ISCO that then performs over two orbits before plunging into the 100 times more massive black hole. We compute the gravitational energy and momenta radiated as well as the fi…
We present a reduced-order surrogate model of gravitational waveforms from non-spinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, \texttt{BHPTNRSur1dq1e4}, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. \texttt{BHPTNRSur1dq1e4} extends an earlier waveform model, \texttt{EMRISur1dq1e4}, by using an updated transition-to-plunge model, covering longer durations up to 30,500 $m_1$ (where $m_1$ is the mass of the primary black hole), includes severa…
The extreme-gravity collisions of binaries with one black hole and one neutron star provide for excellent tests of general relativity. We here study how well one can constrain theories beyond general relativity with additional scalar fields that allow for spontaneous scalarization of neutron stars, and those motivated from string theory. We find that existing bounds can be improved with current gravitational-wave detectors if the black hole mass is sufficiently small. Bounds will further improve by many orders of magnitude with future detections, especially by combining multiple events.
We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in three major areas of BH physics: (i) BHs as sources of gravitational waves (GWs), (ii) astrophysical systems involving BHs, and (iii) BHs in high-energy physics. We conclude with a list of the most urgent tasks for numerical relativity in these three areas.
We perform fully relativistic calculations of binary neutron stars in quasi-equilibrium circular orbits. We integrate Einstein's equations together with the relativistic equation of hydrostatic equilibrium to solve the initial value problem for equal-mass binaries of arbitrary separation. We construct sequences of constant rest mass and identify the innermost stable circular orbit and its angular velocity. We find that the quasi-equilibrium maximum allowed mass of a neutron star in a close binary is slightly larger than in isolation.
Consistency of spin effects between numerical relativity and perturbation theory for inspiraling comparable-mass black hole binaries
Kavli Institute for Theoretical Physics, University of California Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；University of Rhode Island（罗德岛大学）；University of Massachusetts, Dartmouth（马萨诸塞大学达特茅斯分校）
Binary pulsars allow us to carry out precision tests of gravity and have placed stringent bounds on a broad class of theories beyond general relativity. Current and future radio telescopes, such as FAST, SKA, and MeerKAT, may find a new astrophysical system, a pulsar orbiting around a black hole, which will provide us a new source for probing gravity. In this paper, we systematically study the prospects of testing general relativity with such black hole-pulsar binaries. We begin by finding a mapping between generic non-Einsteinian parameters in the orbital decay rate and theoretical constants …
Recent breakthroughs in the field of numerical relativity have led to dramatic progress in understanding the predictions of General Relativity for the dynamical interactions of two black holes in the regime of very strong gravitational fields. Such black-hole binaries are important astrophysical systems and are a key target of current and developing gravitational-wave detectors. The waveform signature of strong gravitational radiation emitted as the black holes fall together and merge provides a clear observable record of the process. After decades of slow progress, these mergers and the gravi…
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The go…
We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the impact of black hole spin on the dynamical formation and evolution of minidisks. We find that during the late inspiral the sizes of minidisks are primarily determined by the interplay between the tidal field and the effective innermost stable orbit around each black hole. Our calculations support that a minidisk forms when the Hill sphere around each black hole is significantly larger than the black hole's effective innermost stable orbit. As the binary inspirals, t…
We review the developments in modeling gravitational recoil from merging black-hole binaries and introduce a new set of 20 simulations to test our previously proposed empirical formula for the recoil. The configurations are chosen to represent generic binaries with unequal masses and precessing spins. Results of these simulations indicate that the recoil formula is accurate to within a few km/s in the similar mass-ratio regime for the out-of-plane recoil.
Gravitational waveforms from the inspiral and ring-down stages of the binary black hole coalescences can be modelled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the non-perturbative merger phase of the binary black-hole coalescence problem. This enables us to \emph{coherently} search for all three stages of the coalescence of non-spinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspir…
