The threshold of black hole formation in axisymmetric vacuum gravity is proving to be more complicated than had been anticipated but, following recent advances, a consensus between independent codes and methods is emerging. Building on earlier work we provide further details of a comparison between three independent numerical codes (the bamps, prague, and sphGR codes), paying special attention to the relative strengths and weaknesses of each and examining various features of near-threshold collapse of vacuum gravitational waves for the first time. In particular, we observe quasi-universal strong-field features appearing in curvature scalars. Focusing on geometric features on the symmetry axis, we construct reference coordinates to aid the comparison of strong-field data. We evolve, for the first time, time-asymmetric wave initial data within the bamps code. To the extent possible with current methods we compare apparent horizons and attempt to determine what causes difficulties in the classification of these strong-field and highly dynamical spacetimes. In all cases the results from the three codes agree very well.

To date, the second-order post-Newtonian (2PN) Hamiltonian has been known in closed analytic form only for systems of up to three point masses. In this paper, we present an analytic expression for the general N -body 2PN Hamiltonian in the Arnowitt-Deser-Misner (ADM) gauge up to a single integral term that, to our knowledge, has no known closed-form analytic solution. We show that the integrals appearing in the 2PN Hamiltonian can be evaluated numerically to machine precision, allowing for cross-validation against analytical results and enabling the full numerical computation of the N -body 2PN Hamiltonian. Furthermore, we demonstrate the practical feasibility of the numerical integration of the equations of motion for N bodies at the 2PN order using different methods and discuss several strategies for improving computational efficiency.

Highly eccentric binary neutron star mergers exhibit unique dynamical and observational signatures compared to quasi-circular ones in terms of their gravitational wave signal and the ejection of matter, leading to different electromagnetic counterparts. In this article, we present general relativistic magneto-hydrodynamic simulations of binary neutron star systems on highly eccentric orbits. While in quasi-circular binaries, the influence of the magnetic field is too weak to affect the general pre-merger dynamics, the close encounters in eccentric systems could potentially trigger magneto-hydrodynamic instabilities. Therefore, we investigate possible effects before, during, and after the merger for a total of three different systems with varying initial eccentricity. We study the f-mode oscillations excited by tidal interaction in close encounters and find good agreement with predicted f-mode frequency estimates. However, our simulations reveal no significant differences compared to results neglecting the magnetic field. Although we observe a rearrangement of the poloidal structure of the magnetic field inside the stars, there is no relevant increase in the magnetic energy during the encounters. Also, during the merger, the amplification of the magnetic field seems to be largely independent of the eccentricity in our systems. Consistent with studies of merging non-magnetized binary neutron stars, we find a correlation between eccentricity and mass ejection, with a higher impact parameter leading to a larger amount of unbound material.

In this proof-of-principle study, we demonstrate the capability of the numerical-relativity code BAM to simulate fully relativistic black-hole binary-single and binary-binary encounters that result in flybys, delayed or accelerated eccentric mergers, exchanges, and other more complex dynamical interactions of initially non-spinning, equal-mass black holes. Our results show that we are able to simulate the time evolution of N black holes in relativistic scattering scenarios, which exhibit interesting dynamics and gravitational-wave signals. The dynamics of these systems show noticeable differences compared to analogous systems in post-Newtonian approximations up to 2.5PN. A key result is that the gravitational waveforms exhibit remarkable features that could potentially make them distinguishable from regular binary mergers.

Binary neutron star mergers are among the most energetic events in our Universe, with magnetic fields significantly impacting their dynamics, particularly after the merger. While numerical-relativity simulations that correctly describe the physics are essential to model their rich phenomenology, the inclusion of magnetic fields is crucial for realistic simulations. For this reason, we have extended the BAM code to enable general relativistic magnetohydrodynamic (GRMHD) simulations employing a hyperbolic "divergence cleaning" scheme. We present a large set of standard GRMHD tests and compare the BAM code to other GRMHD codes, SPRITZ, GRaM-X, and SACRAKK22, which employ different schemes for the evolution of the magnetic fields. Overall, we find that the BAM code shows good performance in simple special-relativistic tests. In addition, we find good agreement and consistent results when comparing GRMHD simulation results between BAM and SACRAKK22.

Simulations of binary collisions involving compact objects require initial data that satisfy the constraint equations of general relativity. For binary boson star simulations it is common practice to use a superposition of two isolated star solutions to construct an approximate solution to the constraint equations. Such superposed data is simple to set up compared to solving these equations explicitly, but also introduces extra constraint violations in the time evolution. In this work we investigate how physical observables depend on the quality of initial data in the case of head-on boson star collisions. In particular we compare results obtained from data prepared using four different methods: the standard method to superpose isolated stars, a heuristic improvement to this superposition technique and two versions of this data where excess constraint violations were removed through a conformal thin-sandwich solver. We find that differences in the time evolutions are dominated by differences in the way the two superposition methods differ, whereas additionally constraint solving the superposed data has smaller impact. The numerical experiments are conducted using the pseudo-spectral code bamps. Our work demonstrates that bamps is a code suited for generating high accuracy numerical waveforms for boson star collisions due to the exponential convergence in the polynomial resolution of the numerical approximation.

Searching the data of gravitational-wave detectors for signals from compact binary mergers is a computationally demanding task. Recently, machine learning algorithms have been proposed to address current and future challenges. However, the results of these publications often differ greatly due to differing choices in the evaluation procedure. The Machine Learning Gravitational-Wave Search Challenge was organized to resolve these issues and produce a unified framework for machine-learning search evaluation. Six teams submitted contributions, four of which are based on machine learning methods and two are state-of-the-art production analyses. This paper describes the submission from the team TPI FSU Jena and its updated variant. We also apply our algorithm to real O3b data and recover the relevant events of the GWTC-3 catalog.

In 2017, the first joint detection of gravitational waves and electromagnetic waves, produced from the merger of a binary neutron star system, inaugurated a new era of multi-messenger astronomy. Due to the strong gravitational fields present in the last stages of the compact binary coalescence, one has to solve Einstein's field equations for a comprehensive study. For this reason, numerical-relativity simulations are an essential tool to correctly describe and study these compact binary mergers. High-performance computing facilities such as HAWK enable us to perform accurate simulations of binary systems by employing our numerical-relativity code BAM. BAM solves the equations of general relativity together with the equations of general-relativistic hydrodynamics. Within our research project, we use numerical-relativity simulations of binary systems to investigate matter at supranuclear densities, to measure the expansion rate of our Universe, and to calibrate theoretical models for the emitted gravitational and electromagnetic waves.

We present the second data release of gravitational waveforms from binary neutron star (BNS) merger simulations performed by the Computational Relativity (CoRe) collaboration. The current database consists of 254 different BNS configurations and a total of 590 individual numerical-relativity simulations using various grid resolutions. The released waveform data contain the strain and the Weyl curvature multipoles up to . They span a significant portion of the mass, mass-ratio, spin and eccentricity parameter space and include targeted configurations to the events GW170817 and GW190425. CoRe simulations are performed with 18 different equations of state, seven of which are finite temperature models, and three of which account for non-hadronic degrees of freedom. About half of the released data are computed with high-order hydrodynamics schemes for tens of orbits to merger; the other half is computed with advanced microphysics. We showcase a standard waveform error analysis and discuss the accuracy of the database in terms of faithfulness. We present ready-to-use fitting formulas for equation of state-insensitive relations at merger (e.g. merger frequency), luminosity peak, and post-merger spectrum.

We study phenomenological features and stability of boson stars in massless and massive scalar-tensor theory of gravity with Damour-Esposito-Farese coupling. This coupling between the tensor and scalar sectors of the theory leads to a phenomenon called spontaneous scalarization, the onset of which we investigate by numerically computing families of boson-star models using shooting and relaxation algorithms. We systematically explore the effects of the theory's coupling, the mass of the gravitational scalar and the choice of the bosonic potential on the structure of weakly and strongly scalarized solutions. Scalarized boson-star models share many common features with neutron stars in the same scalar-tensor theory of gravity. In particular, scalarization can result in boson stars with significantly larger radii and masses, which tend to be energetically favored over their weakly or non-scalarized counterparts. Overall, we find that boson stars are not quite as susceptible to scalarization as neutron stars.

The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating the need for a better gauge choice. Second, the constraint violations to which simulations are susceptible may be too large and force searches to terminate prematurely. This is a particularly serious issue for first order formulations. We want our adaptive pseudospectral code bamps to be a robust tool for the study of critical phenomena so, having encountered both of these difficulties in work on the vacuum setting, we turn here to investigate these issues in the classic context of a spherically symmetric massless scalar field. We suggest two general improvements. We propose a necessary condition for a gauge choice to respect discrete self-similarity (DSS). The condition is not restricted to spherical symmetry and could be verified with any 3+1 formulation. After evaluating common gauge choices against this condition, we suggest a DSS-compatible gauge source function in generalized harmonic gauge (GHG). To control constraint violations, we modify the constraint damping parameters of GHG, adapting them to collapse spacetimes. This allows us to improve our tuning of the critical amplitude for several families of initial data, even going from 6 up to 11 digits. This is the most precise tuning achieved with the first order GHG formulation to date. Consequently, we are able to reproduce the well known critical phenomena as well as competing formulations and methods, clearly observing up to 3 echoes.

We present the second data release of gravitational waveforms from binary neutron star merger simulations performed by the Computational Relativity (CoRe) collaboration. The current database consists of 254 different binary neutron star configurations and a total of 590 individual numerical-relativity simulations using various grid resolutions. The released waveform data contain the strain and the Weyl curvature multipoles up to $\ell=m=4$. They span a significant portion of the mass, mass-ratio,spin and eccentricity parameter space and include targeted configurations to the events GW170817 and GW190425. CoRe simulations are performed with 18 different equations of state, seven of which are finite temperature models, and three of which account for non-hadronic degrees of freedom. About half of the released data are computed with high-order hydrodynamics schemes for tens of orbits to merger; the other half is computed with advanced microphysics. We showcase a standard waveform error analysis and discuss the accuracy of the database in terms of faithfulness. We present ready-to-use fitting formulas for equation of state-insensitive relations at merger (e.g. merger frequency), luminosity peak, and post-merger spectrum.

When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code BAMPS in the form of fully adaptive, physics-agnostic hp refinement. We describe the foundations of mesh refinement in the context of spectral element methods, the precise algorithm used to perform refinement in BAMPS, as well as several indicator functions used to drive it. Finally, we test the performance, scaling, and the accuracy of the code in treating several 1D and 2D example problems, showing clear improvements over static mesh configurations. In particular, we consider a simple nonlinear wave equation, the evolution of a real scalar field minimally coupled to gravity, as well as nonlinear gravitational waves.

We present the results of the first Machine Learning Gravitational-Wave Search Mock Data Challenge (MLGWSC-1). For this challenge, participating groups had to identify gravitational-wave signals from binary black hole mergers of increasing complexity and duration embedded in progressively more realistic noise. The final of the 4 provided datasets contained real noise from the O3a observing run and signals up to a duration of 20 seconds with the inclusion of precession effects and higher order modes. We present the average sensitivity distance and runtime for the 6 entered algorithms derived from 1 month of test data unknown to the participants prior to submission. Of these, 4 are machine learning algorithms. We find that the best machine learning based algorithms are able to achieve up to 95% of the sensitive distance of matched-filtering based production analyses for simulated Gaussian noise at a false-alarm rate (FAR) of one per month. In contrast, for real noise, the leading machine learning search achieved 70%. For higher FARs the differences in sensitive distance shrink to the point where select machine learning submissions outperform traditional search algorithms at FARs $\geq 200$ per month on some datasets. Our results show that current machine learning search algorithms may already be sensitive enough in limited parameter regions to be useful for some production settings. To improve the state-of-the-art, machine learning algorithms need to reduce the false-alarm rates at which they are capable of detecting signals and extend their validity to regions of parameter space where modeled searches are computationally expensive to run. Based on our findings we compile a list of research areas that we believe are the most important to elevate machine learning searches to an invaluable tool in gravitational-wave signal detection.

With an increasing number of expected gravitational-wave detections of binary neutron star mergers, it is essential that gravitational-wave models employed for the analysis of observational data are able to describe generic compact binary systems. This includes systems in which the individual neutron stars are millisecond pulsars for which spin effects become essential. In this work, we perform numerical-relativity simulations of binary neutron stars with aligned and antialigned spins within a range of dimensionless spins of chi similar to [-0.28, 0.58]. The simulations are performed with multiple resolutions, show a clear convergence order and, consequently, can be used to test existing waveform approximants. We find that for very high spins gravitational-wave models that have been employed for the interpretation of GW170817 and GW190425 arc not capable of describing our numerical-relativity dataset. We verify through a full parameter estimation study in which clear biases in the estimate of the tidal deformability and effective spin are present. We hope that in preparation of the next gravitational-wave observing run of the Advanced LIGO and Advanced Virgo detectors our new set of numerical-relativity data can be used to support future developments of new gravitational-wave models.

As a first application of the new adaptive mesh functionality of the pseudospectral numerical relativity code BAMPS, we evolve twist-free, axisymmetric gravitational waves close to the threshold of collapse. We consider six different one-parameter families of Brill wave initial data; two centered and four off-centered families. Of these the latter have not been treated before. Within each family, we tune the parameter towards the threshold of black hole formation. The results for centered data agree with earlier work. Our key results are first, that close to the threshold of collapse the global peak in the curvature appears on the symmetry axis but away from the origin, indicating that in the limit they will collapse around disjoint centers. This is confirmed in three of the six families by explicitly finding apparent horizons around these large curvature peaks. Second, we find evidence neither for strict discrete-self-similarity nor for universal power-law scaling of curvature quantities. Finally, as in Ledvinka and Khirnov???s recent study, we find approximately universal strong curvature features. These features appear multiple times within individual spacetimes close to the threshold and are furthermore present within all six families.

Numerical studies of the dynamics of gravitational systems, e.g., black hole-neutron star systems, require physical and constraint-satisfying initial data. In this article, we present the newly developed pseudospectral code ELLIPTICA, an infrastructure for construction of initial data for various binary and single gravitational systems of all kinds. The elliptic equations under consideration are solved on a single spatial hypersurface of the spacetime manifold. Using coordinate maps, the hypersurface is covered by patches whose boundaries can adapt to the surface of the compact objects. To solve elliptic equations with arbitrary boundary condition, ELLIPTICA deploys a Schur complement domain decomposition method with a direct solver. In this version, we use cubed sphere coordinate maps and the fields are expanded using Chebyshev polynomials of the first kind. Here, we explain the building blocks of ELLIPTICA and the initial data construction algorithm for a black hole-neutron star binary system. We perform convergence tests and evolve the data to validate our results. Within our framework, the neutron star can reach spin values close to breakup with arbitrary direction, while the black hole can have arbitrary spin with dimensionless spin magnitude ???0.8.

Numerical relativity simulations are the only way to calculate exact gravitational waveforms from binary neutron star mergers and to design templates for gravitational-wave astronomy. The accuracy of these numerical calculations is critical in quantifying tidal effects near merger that are currently one of the main sources of uncertainty in merger waveforms. In this work, we explore the use of an entropy-based flux-limiting scheme for high-order, convergent simulations of neutron star spacetimes. The scheme effectively tracks the stellar surface and physical shocks using the residual of the entropy equation thus allowing the use of unlimited central flux schemes in regions of smooth flow. We perform the first neutron star merger simulations with such a method and demonstrate up to fourth-order convergence in the gravitational waveform phase. The scheme reduces the phase error up to a factor five when compared to state-of-the-art high-order characteristic schemes and can be employed for producing faithful tidal waveforms for gravitational-wave modelling.

Compact binary systems emit gravitational radiation which is potentially detectable by current Earth bound detectors. Extracting these signals from the instruments' background noise is a complex problem and the computational cost of most current searches depends on the complexity of the source model. Deep learning may be capable of finding signals where current algorithms hit computational limits. Here we restrict our analysis to signals from non-spinning binary black holes and systematically test different strategies by which training data is presented to the networks. To assess the impact of the training strategies, we re-analyze the first published networks and directly compare them to an equivalent matched-filter search. We find that the deep learning algorithms can generalize low signal-to-noise ratio (SNR) signals to high SNR ones but not vice versa. As such, it is not beneficial to provide high SNR signals during training, and fastest convergence is achieved when low SNR samples are provided early on. During testing we found that the networks are sometimes unable to recover any signals when a false alarm probability $<10^{-3}$ is required. We resolve this restriction by applying a modification we call unbounded Softmax replacement (USR) after training. With this alteration we find that the machine learning search retains $\geq 91.5\%$ of the sensitivity of the matched-filter search down to a false-alarm rate of 1 per month.

The next observing runs of advanced gravitational-wave detectors will lead to a variety of binary neutron star detections and numerous possibilities for multi-messenger observations of binary neutron star systems. In this context a clear understanding of the merger process and the possibility of prompt black hole formation after merger is important, as the amount of ejected material strongly depends on the merger dynamics. These dynamics are primarily affected by the total mass of the binary, however, the mass ratio also influences the postmerger evolution. To determine the effect of the mass ratio, we investigate the parameter space around the prompt-collapse threshold with a new set of fully relativistic simulations. The simulations cover three equations of state and seven mass ratios in the range of $1.0 \leq q \leq 1.75$, with five to seven simulations of binary systems of different total mass in each case. The threshold mass is determined through an empirical relation based on the collapse-time, which allows us to investigate effects of the mass-ratio on the threshold mass and also on the properties of the remnant system. Furthermore, we model effects of mass ratio and equation of state on tidal parameters of threshold configurations.