Evolution of three-dimensional gravitational waves: Harmonic slicing case

Unveiling the Merger Structure of Black Hole Binaries in Generic Planar Orbits

The precise modeling of binary black hole coalescences in generic planar orbits is a crucial step to disentangle dynamical and isolated binary formation channels through gravitational-wave observations. The merger regime of such coalescences exhibits a significantly higher complexity compared to the quasicircular case, and cannot be readily described through standard parametrizations in terms of eccentricity and anomaly. In the spirit of the effective one body formalism, we build on the study of the test-mass limit, and introduce a new modeling strategy to describe the general-relativistic dynamics of two-body systems in generic orbits. This is achieved through gauge-invariant combinations of the binary energy and angular momentum, such as a dynamical "impact parameter" at merger. These variables reveal simple "quasi-universal" structures of the pivotal merger parameters, allowing us to build an accurate analytical representation of generic (bounded and dynamically bounded) orbital configurations. We demonstrate the validity of these analytical relations using 311 numerical simulations of bounded noncircular binaries with progenitors from the RIT and SXS catalogs, together with a custom dataset of dynamical captures generated using the Einstein Toolkit, and test-mass data in bound orbits. Our modeling strategy lays the foundations of accurate and complete waveform models for systems in arbitrary orbits, bolstering observational explorations of dynamical formation scenarios and the discovery of new classes of gravitational wave sources.

Critical Phenomena in the Collapse of Gravitational Waves

Fine-tuning generic but smooth spherically symmetric initial data for general relativity to the threshold of dynamical black hole formation creates arbitrarily large curvatures, mediated by a universal self-similar solution that acts as an intermediate attractor. For vacuum gravitational waves, however, these critical phenomena have been elusive. We present, for the first time, excellent agreement among three independent numerical simulations of this collapse. Surprisingly, we find no universality, and observe approximate self-similarity for some families of initial data but not for others.

Ultimate Black Hole Recoil: What is the Maximum High-Energy Collision Kick?

We performed a series of 1381 full numerical simulations of high energy collision of black holes to search for the maximum recoil velocity after their merger. We consider equal mass binaries with opposite spins pointing along their orbital plane and perform a search of spin orientations, impact parameters, and initial linear momenta to find the maximum recoil for a given spin magnitude s. This spin sequence for s=0.4, 0.7, 0.8, 0.85, 0.9 is then extrapolated to the extreme case, s=1, to obtain an estimated maximum recoil velocity of 28,562±342  km/s, thus approximately bounded by 10% of the speed of light.

Self-Consistent Picture of the Mass Ejection from a One Second Long Binary Neutron Star Merger Leaving a Short-Lived Remnant in a General-Relativistic Neutrino-Radiation Magnetohydrodynamic Simulation

We perform a general-relativistic neutrino-radiation magnetohydrodynamic simulation of a one second-long binary neutron star merger on the Japanese supercomputer Fugaku using about 85 million CPU hours with 20 736 CPUs. We consider an asymmetric binary neutron star merger with masses of 1.2M_{⊙} and 1.5M_{⊙} and a "soft" equation of state SFHo. It results in a short-lived remnant with the lifetime of ≈0.017  s, and subsequent massive torus formation with the mass of ≈0.05M_{⊙} after the remnant collapses to a black hole. For the first time, we find that after the dynamical mass ejection, which drives the fast tail and mildly relativistic components, the postmerger mass ejection from the massive torus takes place due to the magnetorotational instability-driven turbulent viscosity in a single simulation and the two ejecta components are seen in the distributions of the electron fraction and velocity with distinct features.

Well-Posedness of the Four-Derivative Scalar-Tensor Theory of Gravity in Singularity Avoiding Coordinates

We show that the most general scalar-tensor theory of gravity up to four derivatives in 3+1 dimensions is well-posed in a modified version of the CCZ4 formulation of the Einstein equations in singularity-avoiding coordinates. We demonstrate the robustness of our new formulation in practice by studying equal mass black hole binary mergers for different values of the coupling constants. Although our analysis of well-posedness is restricted to cases in which the couplings are small, we find that in simulations we are able to push the couplings to larger values, so that a certain weak coupling condition is order one, without instabilities developing. Our Letter provides the means for such simulations to be undertaken by the many numerical relativity codes that rely on the moving puncture gauge to evolve black hole singularities.

Thinking Outside the Box: Numerical Relativity with Particles

The observation of gravitational waves from compact objects has now become an active part of observational astronomy. For a sound interpretation, one needs to compare such observations against detailed Numerical Relativity simulations, which are essential tools to explore the dynamics and physics of compact binary mergers. To date, essentially all simulation codes that solve the full set of Einstein’s equations are performed in the framework of Eulerian hydrodynamics. The exception is our recently developed Numerical Relativity code SPHINCS_BSSN which solves the commonly used BSSN formulation of the Einstein equations on a structured mesh and the matter equations via Lagrangian particles. We show here, for the first time, SPHINCS_BSSN neutron star merger simulations with piecewise polytropic approximations to four nuclear matter equations of state. In this set of neutron star merger simulations, we focus on perfectly symmetric binary systems that are irrotational and have 1.3 M⊙ masses. We introduce some further methodological refinements (a new way of steering dissipation, an improved particle–mesh mapping), and we explore the impact of the exponent that enters in the calculation of the thermal pressure contribution. We find that it leaves a noticeable imprint on the gravitational wave amplitude (calculated via both quadrupole approximation and the Ψ4 formalism) and has a noticeable impact on the amount of dynamic ejecta. Consistent with earlier findings, we only find a few times 10−3M⊙ as dynamic ejecta in the studied equal mass binary systems, with softer equations of state (which are more prone to shock formation) ejecting larger amounts of matter. In all of the cases, we see a credible high-velocity (∼0.5…0.7c) ejecta component of ∼10−4M⊙ that is launched at contact from the interface between the two neutron stars. Such a high-velocity component has been suggested to produce an early, blue precursor to the main kilonova emission, and it could also potentially cause a kilonova afterglow.

Does Charge Matter in High-Energy Collisions of Black Holes?

We perform numerical-relativity simulations of high-energy head-on collisions of charged black holes with the same charge-to-mass ratio λ. We find that electromagnetic interactions have subdominant effects already at low Lorentz factors γ, supporting the conjecture that the details of the properties of black holes (e.g., their spin or charge) play a secondary role in these phenomena. Using this result and conservation of energy, we argue these events cannot violate cosmic censorship.

Magnetohydrodynamic Simulations of Self-Consistent Rotating Neutron Stars with Mixed Poloidal and Toroidal Magnetic Fields

We perform the first magnetohydrodynamic simulations in full general relativity of self-consistent rotating neutron stars (NSs) with ultrastrong mixed poloidal and toroidal magnetic fields. The initial uniformly rotating NS models are computed assuming perfect conductivity, stationarity, and axisymmetry. Although the specific geometry of the mixed field configuration can delay or accelerate the development of various instabilities known from analytic perturbative studies, all our models finally succumb to them. Differential rotation is developed spontaneously in the cores of our magnetars which, after sufficient time, is converted back to uniform rotation. The rapidly rotating magnetars show a significant amount of ejecta, which can be responsible for transient kilonova signatures. However, no highly collimated, helical magnetic fields or incipient jets, which are necessary for γ-ray bursts, arise at the poles of these magnetars by the time our simulations are terminated.

Neutron Star Mergers and the Quark Matter Equation of State

As neutron stars merge they can approach very high nuclear density. Here, we summarized recent results for the evolution and gravitational wave emission from binary-neutron star mergers using a a variety of nuclear equations of state with and without a crossover transition to quark matter. We discuss how the late time gravitational wave emission from binary neutron star mergers may possibly reveal the existence of a crossover transition to quark matter.

Dynamical Descalarization in Binary Black Hole Mergers

Scalar fields coupled to the Gauss-Bonnet invariant can undergo a tachyonic instability, leading to spontaneous scalarization of black holes. Studies of this effect have so far been restricted to single black hole spacetimes. We present the first results on dynamical scalarization in head-on collisions and quasicircular inspirals of black hole binaries with numerical relativity simulations. We show that black hole binaries can either form a scalarized remnant or dynamically descalarize by shedding off its initial scalar hair. The observational implications of these findings are discussed.

Universality of Curvature Invariants in Critical Vacuum Gravitational Collapse

We report on a numerical study of gravitational waves undergoing gravitational collapse due to their self-interaction. We consider several families of asymptotically flat initial data which, similar to the well-known Choptuik's discovery, can be fine-tuned between dispersal into empty space and collapse into a black hole. We find that near-critical spacetimes exhibit behavior similar to scalar-field collapse: For different families of initial data, we observe universal "echoes" in the form of irregularly repeating, approximate, scaled copies of the same piece of spacetime.

Accretion onto a small black hole at the center of a neutron star

We revisit the system consisting of a neutron star that harbors a small, possibly primordial, black hole at its center, focusing on a nonspinning black hole embedded in a nonrotating neutron star. Extending earlier treatments, we provide an analytical treatment describing the rate of secular accretion of the neutron star matter onto the black hole, adopting the relativistic Bondi accretion formalism for stiff equations of state that we presented elsewhere. We use these accretion rates to sketch the evolution of the system analytically until the neutron star is completely consumed. We also perform numerical simulations in full general relativity for black holes with masses up to nine orders of magnitude smaller than the neutron star mass, including a simulation of the entire evolution through collapse for the largest black hole mass. We construct relativistic initial data for these simulations by generalizing the black hole puncture method to allow for the presence of matter, and evolve these data with a code that is optimally designed to resolve the vastly different length scales present in this problem. We compare our analytic and numerical results, and provide expressions for the lifetime of neutron stars harboring such endoparasitic black holes.

Gravitational waves from disks around spinning black holes: Simulations in full general relativity

We present fully general-relativistic numerical evolutions of self-gravitating tori around spinning black holes with dimensionless spin a/M = 0.7 parallel or antiparallel to the disk angular momentum. The initial disks are unstable to the hydrodynamic Papaloizou-Pringle instability which causes them to grow persistent orbiting matter clumps. The effect of black hole spin on the growth and saturation of the instability is assessed. We find that the instability behaves similarly to prior simulations with nonspinning black holes, with a shift in frequency due to spin-induced changes in disk orbital period. Copious gravitational waves are generated by these systems, and we analyze their detectability by current and future gravitational wave observatories for a large range of masses. We find that systems of 10 M ⊙-relevant for black hole-neutron star mergers-are detectable by Cosmic Explorer out to ~300 Mpc, while DECIGO (LISA) will be able to detect systems of 1000 M ⊙ (105 M ⊙)-relevant for disks forming in collapsing supermassive stars-out to cosmological redshift of z ~ 5 (z ~ 1). Computing the accretion rate of these systems we find that these systems may also be promising sources of coincident electromagnetic signals.

General Relativistic Simulations of the Quasicircular Inspiral and Merger of Charged Black Holes: GW150914 and Fundamental Physics Implications

We perform general-relativistic simulations of charged black holes targeting GW150914. We show that the inspiral is most efficient for detecting black hole charge through gravitational waves and that GW150914 is compatible with having charge-to-mass ratio as high as 0.3. Our work applies to electric and magnetic charge and to theories with black holes endowed with U(1) (hidden or dark) charges. Using our results, we place an upper bound on the deviation from general relativity in the dynamical strong-filed regime of Moffat's modified gravity.

Black hole-neutron star coalescence: Effects of the neutron star spin on jet launching and dynamical ejecta mass

Black hole-neutron star (BHNS) mergers are thought to be sources of gravitational waves (GWs) with coincident electromagnetic (EM) counterparts. To further probe whether these systems are viable progenitors of short gamma-ray bursts (SGRBs) and kilonovas, and how one may use (the lack of) EM counterparts associated with LIGO/Virgo candidate BHNS GW events to sharpen parameter estimation, we study the impact of neutron star spin in BHNS mergers. Using dynamical spacetime magnetohydrodynamic simulations of BHNSs initially on a quasicircular orbit, we survey configurations that differ in the BH spin (a BH/M BH = 0 and 0.75), the NS spin (a NS/M NS = -0.17, 0, 0.23, and 0.33), and the binary mass ratio (q = M BH:M NS = 3:1 and 5:1). The general trend we find is that increasing the NS prograde spin increases both the rest mass of the accretion disk onto the remnant black hole, and the rest mass of dynamically ejected matter. By a time Δt ~ 3500-5500M ~ 88-138(M NS/1.4 M ⊙) ms after the peak gravitational-wave amplitude, a magnetically driven jet is launched only for q = 3:1 regardless of the initial NS spin. The lifetime of the jets [Δt ~ 0.5-0.8(M NS/1.4 M ⊙) s] and their outgoing Poynting luminosity [L Poyn ~ 1051.5±0.5 erg/s] are consistent with typical SGRBs' luminosities and expectations from the Blandford-Znajek mechanism. By the time we terminate our simulations, we do not observe either an outflow or a large-scale magnetic-field collimation for the other systems we consider. The mass range of dynamically ejected matter is 10-4.5-10-2(M NS/1.4 M ⊙) M ⊙, which can power kilonovas with peak bolometric luminosities L knova ~ 1040-1041.4 erg/s with rise times ≲6.5 h and potentially detectable by the LSST.

Neutron star merger remnants

Binary neutron star mergers observations are a unique way to constrain fundamental physics and astrophysics at the extreme. The interpretation of gravitational-wave events and their electromagnetic counterparts crucially relies on general-relativistic models of the merger remnants. Quantitative models can be obtained only by means of numerical relativity simulations in 3 + 1 dimensions including detailed input physics for the nuclear matter, electromagnetic and weak interactions. This review summarizes the current understanding of merger remnants focusing on some of the aspects that are relevant for multimessenger observations.

Magnetohydrodynamic simulations of binary neutron star mergers in general relativity: Effects of magnetic field orientation on jet launching

Binary neutron star mergers can be sources of gravitational waves coincident with electromagnetic counterpart emission across the spectrum. To solidify their role as multimessenger sources, we present fully 3D, general relativistic, magnetohydrodynamic simulations of highly spinning binary neutrons stars initially on quasicircular orbits that merge and undergo delayed collapse to a black hole. The binaries consist of two identical stars modeled as Γ = 2 polytropes with spin χ NS = 0.36 aligned along the direction of the total orbital angular momentum L. Each star is initially threaded by a dynamical unimportant interior dipole magnetic field. The field is extended into the exterior where a nearly force-free magnetosphere resembles that of a pulsar. The magnetic dipole moment μ is either aligned or perpendicular to L and has the same initial magnitude for each orientation. For comparison, we also impose symmetry across the orbital plane in one case where μ in both stars is aligned along L. We find that the lifetime of the transient hypermassive neutron star remnant, the jet launching time, and the ejecta (which can give rise to a detectable kilonova) are very sensitive to the magnetic field orientation. By contrast, the physical properties of the black hole + disk remnant, such as the mass and spin of the black hole, the accretion rate, and the electromagnetic (Poynting) luminosity, are roughly independent of the initial magnetic field orientation. In addition, we find imposing symmetry across the orbital plane does not play a significant role in the final outcome of the mergers. Our results suggest that, as in the black hole-neutron star merger scenario, an incipient jet emerges only when the seed magnetic field has a sufficiently large-scale poloidal component aligned to the initial orbital angular momentum. The lifetime [Δt ≳ 140(M NS/1.625 M ⊙) ms] and Poynting luminosities [L EM ≃ 1052 erg/s] of the jet, when it forms, are consistent with typical short gamma-ray bursts, as well as with the Blandford-Znajek mechanism for launching jets.

Great Impostors: Extremely Compact, Merging Binary Neutron Stars in the Mass Gap Posing as Binary Black Holes

Can one distinguish a binary black hole undergoing a merger from a binary neutron star if the individual compact companions have masses that fall inside the so-called mass gap of 3-5  M_{⊙}? For neutron stars, achieving such masses typically requires extreme compactness and in this work we present initial data and evolutions of binary neutron stars initially in quasiequilibrium circular orbits having a compactness C=0.336. These are the most compact, nonvacuum, quasiequilibrium binary objects that have been constructed and evolved to date, including boson stars. The compactness achieved is only slightly smaller than the maximum possible imposed by causality, C_{max}=0.355, which requires the sound speed to be less than the speed of light. By comparing the emitted gravitational waveforms from the late inspiral to merger and postmerger phases between such a binary neutron star vs a binary black hole of the same total mass we identify concrete measurements that serve to distinguish them. With that level of compactness, the binary neutron stars exhibit no tidal disruption up until merger, whereupon a prompt collapse is initiated even before a common core forms. Within the accuracy of our simulations the black hole remnants from both binaries exhibit ringdown radiation that is not distinguishable from a perturbed Kerr spacetime. However, their inspiral leads to phase differences of the order of ∼5  rad over an ∼81  km separation (1.7 orbits) while typical neutron stars exhibit phase differences of ≥20  rad. Although a difference of ∼5  rad can be measured by current gravitational wave laser interferometers (e.g., aLIGO/Virgo), uncertainties in the individual masses and spins will likely prevent distinguishing such compact, massive neutron stars from black holes.

Dynamically Stable Ergostars Exist: General Relativistic Models and Simulations

We construct the first dynamically stable ergostars (equilibrium neutron stars that contain an ergoregion) for a compressible, causal equation of state. We demonstrate their stability by evolving both strict and perturbed equilibrium configurations in full general relativity for over a hundred dynamical timescales (≳30 rotational periods) and observing their stationary behavior. This stability is in contrast to earlier models which prove radially unstable to collapse. Our solutions are highly differentially rotating hypermassive neutron stars with a corresponding spherical compaction of C=0.3. Such ergostars can provide new insights into the geometry of spacetimes around highly compact, rotating objects and on the equation of state at supranuclear densities. Ergostars may form as remnants of extreme binary neutron star mergers and possibly provide another mechanism for powering short gamma-ray bursts.

Critical Phenomena in the Gravitational Collapse of Electromagnetic Waves

We numerically investigate the threshold of black-hole formation in the gravitational collapse of electromagnetic waves in axisymmetry. We find approximate power-law scaling ρ_{max}∼(η_{*}-η)^{-2γ} of the maximum density in the time evolution of near-subcritical data with γ≃0.145, where η is the amplitude of the initial data. We directly observe approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of Δ≃0.55. The critical solution is approximately the same for two families of initial data, providing some evidence of universality. Neither the discrete self-similarity nor the universality, however, are exact. We speculate that the absence of an exactly discrete self-similarity might be caused by the interplay of electromagnetic and gravitational wave degrees of freedom, or by the presence of higher-order angular multipoles, or both, and discuss implications of our findings for the critical collapse of vacuum gravitational waves.

Detecting the Hadron-Quark Phase Transition with Gravitational Waves

The long-awaited detection of a gravitational wave from the merger of a binary neutron star in August 2017 (GW170817) marks the beginning of the new field of multi-messenger gravitational wave astronomy. By exploiting the extracted tidal deformations of the two neutron stars from the late inspiral phase of GW170817, it is now possible to constrain several global properties of the equation of state of neutron star matter. However, the most interesting part of the high density and temperature regime of the equation of state is solely imprinted in the post-merger gravitational wave emission from the remnant hypermassive/supramassive neutron star. This regime was not observed in GW170817, but will possibly be detected in forthcoming events within the current observing run of the LIGO/VIRGO collaboration. Numerous numerical-relativity simulations of merging neutron star binaries have been performed during the last decades, and the emitted gravitational wave profiles and the interior structure of the generated remnants have been analysed in detail. The consequences of a potential appearance of a hadron-quark phase transition in the interior region of the produced hypermassive neutron star and the evolution of its underlying matter in the phase diagram of quantum cromo dynamics will be in the focus of this article. It will be shown that the different density/temperature regions of the equation of state can be severely constrained by a measurement of the spectral properties of the emitted post-merger gravitational wave signal from a future binary compact star merger event.

Numerical relativity of compact binaries in the 21st century

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, with increasingly sophisticated treatment of fluids, electromagnetic fields, and neutrino radiation. However, it was not until 2005 that accurate long-term evolutions of binaries containing black holes were even possible (Pretorius 2005 Phys. Rev. Lett. 95 121101, Campanelli et al 2006 Phys. Rev. Lett. 96 111101, Baker et al 2006 Phys. Rev. Lett. 96 111102). Since then, there has been an explosion of new results and insights into the physics of strongly-gravitating system. Particular emphasis has been placed on understanding the gravitational wave and electromagnetic signatures from these extreme events. And with the recent dramatic discoveries of gravitational waves from merging black holes by the Laser Interferometric Gravitational Wave Observatory and Virgo, and the subsequent discovery of both electromagnetic and gravitational wave signals from a merging neutron star-neutron star binary, numerical relativity became an indispensable tool for the new field of multimessenger astronomy.

Simulating the magnetorotational collapse of supermassive stars: Incorporating gas pressure perturbations and different rotation profiles

Collapsing supermassive stars (SMSs) with masses M ≳ 104-6 M ⊙ have long been speculated to be the seeds that can grow and become supermassive black holes (SMBHs). We previously performed general relativistic magnetohydrodynamic (GRMHD) simulations of marginally stable Γ = 4/3 polytropes uniformly rotating at the mass-shedding limit and endowed initially with a dynamically unimportant dipole magnetic field to model the direct collapse of SMSs. These configurations are supported entirely by thermal radiation pressure and reliably model SMSs with M ≳ 106 M ⊙. We found that around 90% of the initial stellar mass forms a spinning black hole (BH) remnant surrounded by a massive, hot, magnetized torus, which eventually launches a magnetically-driven jet. SMSs could be therefore sources of ultra-long gamma-ray bursts (ULGRBs). Here we perform GRMHD simulations of Γ ≳ 4/3, polytropes to account for the perturbative role of gas pressure in SMSs with M ≲ 106 M ⊙. We also consider different initial stellar rotation profiles. The stars are initially seeded with a dynamically weak dipole magnetic field that is either confined to the stellar interior or extended from its interior into the stellar exterior. We calculate the gravitational wave burst signal for the different cases. We find that the mass of the black hole remnant is 90%-99% of the initial stellar mass, depending sharply on Γ - 4/3 as well as on the initial stellar rotation profile. After t ~ 250-550M ≈ 1 - 2 × 103(M/106 M ⊙) s following the appearance of the BH horizon, an incipient jet is launched and it lasts for ~104-105(M/106 M ⊙) s, consistent with the duration of long gamma-ray bursts. Our numerical results suggest that the Blandford-Znajek mechanism powers the incipient jet. They are also in rough agreement with our recently proposed universal model that estimates accretion rates and electromagnetic (Poynting) luminosities that characterize magnetized BH-disk remnant systems that launch a jet. This model helps explain why the outgoing electromagnetic luminosities computed for vastly different BH-disk formation scenarios all reside within a narrow range (~1052±1 erg s-1), roughly independent of M.

Fundamentals of numerical relativity for gravitational wave sources

Einstein's theory of general relativity affords an enormously successful description of gravity. The theory encodes the gravitational interaction in the metric, a tensor field on spacetime that satisfies partial differential equations known as the Einstein equations. This review introduces some of the fundamental concepts of numerical relativity-solving the Einstein equations on the computer-in simple terms. As a primary example, we consider the solution of the general relativistic two-body problem, which features prominently in the new field of gravitational wave astronomy.