We analytically solve the constraints in General Relativity for two black holes with arbitrary momenta and spin up to third order in these parameters. We compute the location and geometry of the apparent horizon, which depend on the spins, momenta, relative orientation angles, and the separation between the black holes, and present the result in a coordinate-independent form. We also extract the ADM mass and the irreducible mass and verify their consistency. The final expressions are depicted in a coordinate-independent form. The results can be easily extended to any number of black holes and used to complement numerical relativity simulations.
Because they are likely to accrete substantial amounts of interstellar gas, merging supermassive binary black holes are expected to be strong multimessenger sources, radiating gravitational waves, photons from thermal gas, and photons from relativistic electrons energized by relativistic jets. Here we report on a numerical simulation that covers the late inspiral, merger, and initial postmerger phase of such a system where both black holes have the same mass and spin, and both spin axes are parallel to the orbital angular momentum. The simulation incorporates both 3D general relativistic magnetohydrodynamics and numerical relativity. The thermal photon power during the late inspiral, merger, and immediate postmerger phases is drawn from strong shocks rather than dissipation of turbulence inside a smoothly structured accretion disk as typically found around accreting single black holes. We find that the thermal photon and jet Poynting flux outputs are closely related in time, and we posit a mechanism that enforces this relation. The power radiated in both photons and jets diminishes gradually as merger is approached, but jumps sharply at merger to a noisy plateau. Such a distinct lightcurve should aid efforts to identify supermassive black hole mergers, with or without accompanying gravitational wave detections.
Merger gravitational waves from binary black hole coalescence carry rich information about the underlying spacetime dynamics. We analyze merger waves from comparable-mass and extreme-mass-ratio binaries, obtained from numerical relativity and black-hole perturbation theory, respectively, and argue that they are dominated by the prompt wave emissions as the black holes collide. This signal, which we refer to as the direct wave, is modulated by the plunging motion and selectively screened by the gravitational potential of the remnant black hole. The direct wave typically exhibits a time-dependent frequency and decay rate, but for high-spin remnants $(\gtrsim0.7)$ the ergosphere renders it mode-like, with a quasi-stable instantaneous oscillation frequency close to the superradiant frequency. We further estimate its detectability in a GW150914-like system and find that the signal-to-noise ratio can exceed $\sim 10$ with the current ground-based detector network. Our results therefore identify the direct wave as a robust observable for analyzing black hole ringdowns in current and future gravitational wave events.
We investigate the impact of gravitational-wave (GW) recoil on the growth of supermassive black holes (SMBHs) in the early Universe. Forming ~10^9 Msun SMBHs by z ~ 6 is challenging and may require hierarchical mergers of smaller seed black holes. We extend a semi-analytic seed model (Sassano et al. 2021) by explicitly incorporating GW recoil physics. Our model includes: (1) recoil velocity formulae calibrated to numerical relativity for spinning, unequal-mass BH binaries (Campanelli et al. 2007; Lousto et al. 2012); (2) assignment of spin magnitudes and orientations based on seed type (Pop III remnant, stellar cluster, or direct-collapse); and (3) a retention probability scheme comparing the recoil speed to the host halo escape velocity. We find that including GW recoil reduces final SMBH masses by ~20-30% by z = 6 and creates a population of off-nuclear ("wandering") BHs amounting to a few percent of the total. Observable consequences include spatial offsets ~0.1 arcsec and line-of-sight velocity shifts ~10^2-10^3 km/s in a few percent of high-z quasars. All code is publicly available at https://github.com/SMALLSCALEDEV/Black-hole-Recoil-Effects
We model the short gamma-ray bursts (GRB) 090510 as the product of a magnetized neutron star (NS) binary merger. Accounting for the NS critical mass constraint given by the mass of PSR J0952--0607, we infer that GRB 090510 was a highly-magnetized NS-NS merger that left as remnant a Kerr black hole (BH) of $2.4 M_\odot$ with a low-mass accretion disk. The gamma-ray precursor is powered by the magnetic energy released during the merger of the NSs. The prompt emission originates at the transparency of an ultra-relativistic $e^+e^-$ pair-plasma produced by the overcritical electric field induced by the rotating strong magnetic field around the merged object before it reaches the critical mass, the GeV emission by the extractable energy of the newborn BH, and the X-ray afterglow by accretion onto it. We derive the masses of the merging NSs, their magnetic fields, the BH mass, spin, and irreducible mass, the strength of the magnetic field, the disk mass, and obtain an estimate of the gravitational-wave emission during the merger phase preceding the prompt short GRB emission. The inferred parameters agree with up-to-date numerical relativity simulations, confirming that strong magnetic fields above $10^{14}$ G develop in NS-NS mergers and that mergers leading to a central BH remnant have low-mass disks of $\sim 10^{-2} M_\odot$. We also advance the possibility that quasi-period oscillations of tens of Hz of frequency due to Lense-Thirring precession of the matter surrounding the merged object before BH formation can explain the successive spikes following the prompt emission peak.
The binary black hole signal GW250114, the loudest gravitational wave detected to date, offers a unique opportunity to test Einstein's general relativity (GR) in the high-velocity, strong-gravity regime and probe whether the remnant conforms to the Kerr metric. Upon perturbation, black holes emit a spectrum of damped sinusoids with specific, complex frequencies. Our analysis of the post-merger signal shows that at least two quasi-normal modes are required to explain the data, with the most damped remaining statistically significant for about one cycle. We probe the remnant's Kerr nature by constraining the spectroscopic pattern of the dominant quadrupolar ($\ell = m = 2$) mode and its first overtone to match the Kerr prediction to tens of percent at multiple post-peak times. The measured mode amplitudes and phases agree with a numerical-relativity simulation having parameters close to GW250114. By fitting a parameterized waveform that incorporates the full inspiral-merger-ringdown sequence, we constrain the fundamental $(\ell=m=4)$ mode to tens of percent and bound the quadrupolar frequency to within a few percent of the GR prediction. We perform a suite of tests -- spanning inspiral, merger, and ringdown -- finding constraints that are comparable to, and in some cases 2-3 times more stringent than those obtained by combining dozens of events in the fourth Gravitational-Wave Transient Catalog. These results constitute the most stringent single-event verification of GR and the Kerr nature of black holes to date, and outline the power of black-hole spectroscopy for future gravitational-wave observations.
When numerically solving Einstein's equations for binary black holes (BBH), we must find initial data on a three-dimensional spatial slice by solving constraint equations. The construction of initial data is a multi-step process, in which one first chooses freely specifiable data that define a conformal background and impose boundary conditions. Then, one numerically solves elliptic equations and calculates physical properties such as horizon masses, spins, and asymptotic quantities from the solution. To achieve desired properties, one adjusts the free data in an iterative ``control'' loop. Previous methods for these iterative adjustments rely on Newtonian approximations and do not allow the direct control of total energy and angular momentum of the system, which becomes particularly important in the study of hyperbolic encounters of black holes. Using the $SpECTRE$ code, we present a novel parameter control procedure that benefits from Broyden's method in all controlled quantities. We use this control scheme to minimize drifts in bound orbits and to enable the construction of hyperbolic encounters. We see that the activation of off-diagonal terms in the control Jacobian gives us better efficiency when compared to the simpler implementation in the Spectral Einstein Code ($SpEC$). We demonstrate robustness of the method across extreme configurations, including spin magnitudes up to $ḩi = 0.9999$, mass ratios up to $q = 50$, and initial separations up to $D_0 = 1000M$. Given the open-source nature of $SpECTRE$, this is the first time a parameter control scheme for constructing bound and unbound BBH initial data is available to the numerical-relativity community.
The ringdown phase of the binary black hole (BBH) merger provides a clean and direct probe of strong-field gravity and tests of the nature of black holes. The quasinormal mode (QNM) frequencies in modified gravity theories, as well as their amplitudes and phases, might deviate from the Kerr ones in general relativity. Charged black holes (BHs) in Einstein-Maxwell theory provide an excellent example of a beyond-Kerr solution with direct astrophysical and fundamental physics applications. In this work, we extract the ringdown mode amplitudes and phases for charged BBH mergers based on fully general relativistic simulations with charge-to-mass ratio up to 0.3. Our results suggest that even though the inspiral phase of charged BBHs can be significantly accelerated or decelerated, the ringdown mode excitation only changes mildly. We further explore the charge detectability with the ringdown-only signal for the Einstein Telescope and Cosmic Explorer. We find that previous studies may have overestimated the charge detectability and including higher modes in charged waveforms is necessary for future ringdown analysis. This constitutes the first such analysis based on waveforms generated by numerical relativity simulations of charged BHs in full Einstein-Maxwell theory.
The effective one-body (EOB) theory provides an innovative framework for analyzing the dynamics of binary systems, as articulated by Hamilton's equations. This paper investigates a self-consistent EOB theory specifically tailored for the dynamics of such systems. Our methodology begins by emphasizing how to effectively utilize the metrics derived from scattering angles in the analysis of binary black hole mergers. We then construct an effective Hamiltonian and formulate a decoupled, variable-separated Teukolsky-like equation for $\psi^B_4$. Furthermore, we present the formal solution to this equation, detailing the energy flux, radiation-reaction force (RRF), and waveforms for the ``plus" and ``cross" modes generated by spinless binaries. Finally, we carry out numerical calculations using the EOB theory and compare the results with numerical relativity (NR) data from the SXS collaboration. The results indicate that to the innermost stable circular orbit, the binding energy -- angular momentum relation differs from the NR results by less than $5$\textperthousand, with a larger mass ratio yielding better agreement.
We release the first Numerical Relativity catalog of Institut de Ciencies del Cosmos at University of Barcelona (ICCUB) consisting of 128 simulations for black hole binaries. All simulations in this first release correspond to highly eccentric binaries with eccentricity $e = (0.62,0.79)$ which develop zoom-whirls up to three close passages before merger. We consider aligned, equal spin configurations in the range $ḩi = (-0.5, 0.5)$ and equal mass ratios. For each simulation, we provide the modes $(\ell, m)$ of Weyl scalar $\psi_4^{(\ell,m)}$ extrapolated to $r = \infty$, with $\ell \leq 4$. In addition, we provide the corresponding strain modes obtained by computing a double time integral of the Weyl scalar modes. Moreover, we provide metadata and the parameter files required to reproduce our results using the open-source code Einstein Toolkit. A Python code that facilitates the access to the data is available on Git-Hub.
We analyze the spherical harmonic mode amplitudes of quasi-circular, nonprecessing binary black hole mergers using 283 numerical relativity (NR) simulations from the SXS, RIT, and MAYA catalogs. We construct fits using the leading-order post-Newtonian (PN) dependence on intrinsic parameters, replacing the PN velocity with fit coefficients. We compare these to polynomial fits in symmetric mass ratio and spin. We analyze $(\ell, m)$ modes with $\ell \leq 4$ from late inspiral ($t = -500M$ relative to the $(2,2)$ peak) to post-merger ($t = 40M$). For nonspinning systems, the $(2,2)$, $(2,1)$, and $(3,3)$ modes retain the leading-order PN dependence on mass ratio throughout the merger. Higher-order modes deviate from the PN dependence only near and after the merger, where polynomial fits of degree $N \leq 3$ can capture the amplitude behavior up to $40M$. For aligned-spin systems at fixed mass ratio, the $(2,1)$ mode retains its PN spin dependence, while the $(3,2)$ and $(4,3)$ modes exhibit a quadratic spin dependence near merger. The PN-inspired fits lose accuracy with increasing mass ratio, particularly near merger. Results broadly agree across catalogs, though discrepancies appear in the $(3,1)$, $(4,2)$, and $(4,1)$ modes, likely from resolution differences. Our results clarify the extent to which PN structure persists in mode amplitudes and show that simple polynomial models can capture strong-field behavior near merger, enabling efficient and interpretable waveform modeling in this regime.
High-fidelity gravitational waveform models are essential for realizing the scientific potential of next-generation gravitational-wave observatories. While highly accurate, state-of-the-art models often rely on extensive phenomenological calibrations to numerical relativity (NR) simulations for the late-inspiral and merger phases, which can limit physical insight and extrapolation to regions where NR data is sparse. To address this, we introduce the Spinning Effective-to-Backwards One Body (SEBOB) formalism, a hybrid approach that combines the well-established Effective-One-Body (EOB) framework with the analytically-driven Backwards-One-Body (BOB) model, which describes the merger-ringdown from first principles as a perturbation of the final remnant black hole. We present two variants building on the state-of-the-art $SEOBNRv5HM$ model: $seobnrv5_nrnqc_bob$, which retains standard NR-calibrated non-quasi-circular (NQC) corrections and attaches a BOB-based merger-ringdown; and a more ambitious variant, $seobnrv5_bob$, which uses BOB to also inform the NQC corrections, thereby reducing reliance on NR fitting and enabling higher-order ($\mathcal{C}^2$) continuity by construction. Implemented in the open-source $NRPy$ framework for optimized C-code generation, the SEBOB model is transparent, extensible, and computationally efficient. By comparing our waveforms to a large catalog of NR simulations, we demonstrate that SEBOB yields accuracies comparable to the highly-calibrated $SEOBNRv5HM$ model, providing a viable pathway towards more physically motivated and robust waveform models
Black hole spectroscopy is an important pillar when studying gravitational waves from black holes and enables tests of general relativity. Most of the gravitational-wave signals observed over the last decade originate from binary black hole systems. Binary neutron star or black hole-neutron star systems are rarer but of particular interest for the next-generation ground-based gravitational-wave detectors. These events offer the exciting possibility of studying matter effects on the ringdown of "dirty black holes". In this work, we ask the question: Does matter matter? Using numerical-relativity, we simulate a wide range of collapsing neutron stars producing matter environments, both in isolated scenarios and in binary mergers. Qualitatively, the resulting ringdown signals can be classified into "clean", "modified", and "distorted" cases, depending on the amount of matter that is present. We apply standard strategies for extracting quasinormal modes of clean signals, using both theory-agnostic and theory-specific assumptions. Even in the presence of matter, possible modifications of quasinormal modes seem to be dominated by ringdown modeling systematics. We find that incorporating multiple quasinormal modes allows one to drastically reduce mismatches and errors in estimating the final black hole mass at early times. If not treated carefully, deviations in the fundamental quasinormal mode might artificially be overestimated and falsely attributed to the presence of matter or violations of general relativity.
GW200105_162426 is the first neutron star-black hole merger to be confidently confirmed through either gravitational-wave or electromagnetic observations. Although initially analyzed after detection, the event has recently gained renewed attention following a study, Morras et al. (2025), that employed a post-Newtonian inspiral-only waveform model and reported strong evidence for orbital eccentricity. In this work, we perform a detailed analysis of GW200105 using state-of-the-art effective-one-body waveform models. Importantly, we present the first study of this event utilizing a physically complete model that incorporates both orbital eccentricity and spin precession across the full inspiral, merger, and ringdown stages, along with higher-order gravitational wave modes. Our results support the presence of eccentricity in the signal, with zero eccentricity excluded from $99%$ credible interval, but yield a mass ratio closer to the original LIGO-Virgo-KAGRA analysis, differing from the findings of Morras et al. (2025). Additionally, similar to previous eccentric-only analysis Planas et al. (2025), we observe a multimodal structure in the eccentricity posterior distribution. We conduct targeted investigations to understand the origin of this multimodality and complement our analysis with numerical relativity simulations to examine how the inclusion of eccentricity impacts the merger dynamics.
Recent advances in post-Minkowskian (PM) gravity provide new avenues for the high precision modelling of compact binaries. In conjunction with the Effective One Body (EOB) formalism, highly accurate PM informed models of binary black holes on scattering trajectories have emerged. Several complementary approaches currently exist, in particular the SEOB-PM model, the $w_{\rm eob}$ framework and the recent LEOB approach. These models incorporate PM results in fundamentally different ways, employing distinct resummation schemes and gauge choices. Notably, both SEOB-PM and LEOB have been used to compute gravitational waves of bound systems, showing excellent agreement with numerical relativity (NR). The essential component to all of the models is the EOB mass-shell condition describing the dynamics of the two-body spacetime. In this work we will investigate how this mass-shell condition is constructed, paying particular attention to the impact of gauge choices and how they interact with different resummation schemes, showing that there is a strong dependence on both coordinate choice and EOB gauge. For the region of parameter space considered, we find that the best performing gauges coincide with the choices made in SEOB-PM and $w_{eob}$, with other choices exhibiting worse performance. The case of spinning black holes is also considered, where the current techniques for spinning EOB-PM are reviewed and compared. We also introduce a new gauge based upon the centrifugal radius, which improves upon previous models, particularly for large and negative spins. This offers a promising avenue for further resummation of spin information within the EOB-PM framework.
We study the nonlinear radial stability of boson stars with a solitonic potential across the entire parameter space, focusing especially on families of solutions that support ultracompact models on the perturbatively stable branch. Using a dimensional reduction of the CCZ4 formulation of numerical relativity, we dynamically evolve these models with both internal and external perturbations. We find in particular that there are perturbatively stable models with positive binding energy that do not effectively disperse even under explicit perturbations, challenging the conventional wisdom that negative binding energy is a necessary condition for the dynamical stability of boson stars and other compact objects.
We reinvestigate the stability properties of ultracompact spinning boson stars with a stable light ring using fully nonlinear 3+1 and 2+1 numerical relativity simulations and two different formulations of the Einstein equations. We find no evidence of an instability on timescales of $t \mu \sim 10^4$ (in units of the scalar mass), when allowing the star to be perturbed either solely by discretization error or by imposing various types of perturbations to our initial data. We find that the initially imposed perturbations exhibit slow decay, even for magnitudes just below the order where immediate collapse is induced.
We report the performance of a newly implemented fourth-order accurate finite-volume HLLC Riemann solver in the adaptive-mesh-refinement numerical relativity code {\tt SACRA-MPI}. First, we validate our implementation in one-dimensional special relativistic hydrodynamics tests, i.e., a simple wave and shock tube test, which have analytic solutions. We demonstrate that the fourth-order convergence is achieved for the smooth flow, which cannot be achieved in our original second-order accurate finite-volume Riemann solver. We also show that our new solver is robust for the strong shock wave emergence problem. Second, we validate the implementation in a dynamical spacetime by demonstrating that {\tt SACRA-MPI} perfectly preserves the $\pi$-symmetry without imposing the $\pi$-symmetry in a short-term ($\sim 20~{\rm ms}$ in the inspiral and subsequent post-merger phase) non-spinning equal-mass binary neutron star merger simulations. Finally, we quantify the accuracy of $\approx 28$ cycles inspiral gravitational waveforms from binary neutron star mergers by conducting a resolution study with $\approx 78, 94$, $118$, and $135$ m. We find that the fourth-order accurate Riemann solver achieves the convergence order $\approx 2.1\pm{0.05}$--$2.4\pm{0.27}$, i.e., slightly evolving with time, in the inspiral gravitational wave phase, while the second-order accurate Riemann solver achieves the convergence order $\approx 2.0\pm{0.5}$. The residual phase error towards the continuum limit at the merger is $0.27\pm 0.07$ rad and $0.58\pm 0.22$ rad out of a total phase of $\approx 176$ rad, respectively, for the fourth- and second-order accurate Riemann solver.
We describe a series of laboratory experiments that can be performed with the Quantum Control apparatus sold by TeachSpin, which uses pulsed NMR techniques to observe the precession of protons in a liquid water sample. With a uniform background magnetic field of 21 Gauss, the protons precess at about 90 kHz, yielding numerous relatively simple observations and measurements that are well suited to undergraduate physics teaching labs. Our goal in this paper is to document some of these experiments in detail, thereby making it easier for instructors to choose material that is best suited for their curricula.
Gravitational Waves (GWs) provide a powerful means for cosmological distance estimation, circumventing the systematic uncertainties associated with traditional electromagnetic (EM) indicators. This work presents a model for estimating distances to binary black hole (BBH) mergers using only GW data, independent of EM counterparts or galaxy catalogs. By utilizing the intrinsic properties of the GW signal, specifically the strain amplitude and merger frequency, our model offers a computationally efficient preliminary distance estimation approach that could complements existing Bayesian parameter estimation pipelines. In this work, we examine a simplified analytical expression for the GW luminosity distance derived from General Relativity (GR), based on the leading-order quadrupole approximation. Without incorporating post-Newtonian (PN) or numerical relativity (NR) corrections, or modeling spin, eccentricity, or inclination, we test how closely this expression can reproduce distances reported by full Bayesian inference pipelines. We apply our model to 87 events from the LIGO-Virgo-Kagra (LVK) Gravitational Wave Transient Catalogues (GWTC), computing distances for these sources. Our results demonstrate consistent agreement with GWTC-reported distances, further supported by graphical comparisons that highlight the model's performance across multiple events.
GW230529_181500 represented the first gravitational-wave detection with one of the component objects' mass inferred to lie in the previously hypothesized mass gap between the heaviest neutron stars and the lightest observed black holes. Given the expected maximum mass values for neutron stars, this object was identified as a black hole, and, with the secondary component being a neutron star, the detection was classified as a neutron star-black hole merger. However, due to the low signal-to-noise ratio and the known waveform degeneracy between the spin and mass ratio in the employed gravitational-wave models, GW230529_181500 could also be interpreted as a merger of two heavy ($\gtrsim 2 \mathrm{M}_\odot$) neutron stars with high spins. We investigate the distinguishability of these scenarios by performing parameter estimation on simulated signals obtained from numerical-relativity waveforms for both neutron star-black hole and binary neutron star systems, with parameters consistent with GW230529_181500, and comparing them to the analysis of the real event data. We find that GW230529_181500 is more likely to have originated from a neutron star-black hole merger, though the possibility of a binary neutron star origin can not be ruled out. Moreover, we use the simulation data to estimate the signatures of potential electromagnetic counterparts emitted by the systems. We find them to be too dim to be located by current wide-field surveys if only the dynamical ejecta is considered, and detectable by the Vera C. Rubin Observatory during the first two days after merger if one accounts for additional disk wind ejecta.
In the field of gravitational wave science, next-generation detectors will be substantially more accurate than the current suite of detectors. Numerical relativity simulations of binary black hole (BBH) gravitational waveforms must become faster, more efficient, and more accurate to be used in analyses of these next-generation detections. One approach, which the $SpECTRE$ code employs, is using spectral methods for accuracy along with asynchronous task-based parallelism to avoid idle time in simulations and make the most efficient use of computational resources. When writing an asynchronous application, algorithms must be redesigned compared to their synchronous counterparts. To illustrate this process, we present novel methods for dynamically tracking the apparent horizons in evolutions of BBH mergers using a feedback control system, all in the context of asynchronous parallelism. We also briefly detail how these methods can be applied to binary neutron star simulations performed with asynchronous parallelism.
We present a comprehensive assessment of multiparameter tests of general relativity (GR) in the inspiral regime of compact binary coalescences using Principal Component Analysis (PCA). Our analysis is based on an extensive set of simulated gravitational wave signals, including both general relativistic and non-GR sources, injected into zero-noise data colored by the noise power spectral densities of the LIGO and Virgo detectors at their designed sensitivities. We evaluate the performance of PCA-based methods in the context of two established frameworks: TIGER and FTI. For GR-consistent signals, we find that PCA enables stringent constraints on potential deviations from GR, even in the presence of multiple free parameters. Applying the method to simulated signals that explicitly violate GR, we demonstrate that PCA is effective at identifying such deviations. We further test the method using numerical relativity waveforms of eccentric binary black hole systems and show that missing physical effects-such as orbital eccentricity-can lead to apparent violations of GR if not properly included in the waveform models used for analysis. Finally, we apply our PCA-based test to selected real gravitational-wave events from GWTC-3, including GW190814 and GW190412. We present joint constraints from selected binary black hole events in GWTC-3, finding that the 90% credible bound on the most informative PCA parameter is $0.03^{+0.08}_{-0.08}$ in the TIGER framework and $-0.01^{+0.05}_{-0.04}$ in the FTI framework, both of which are consistent with GR. These results highlight the sensitivity and robustness of the PCA-based approach and demonstrate its readiness for application to future observational data from the fourth observing runs of LIGO, Virgo, and KAGRA.
We present a framework to propagate to null infinity gravitational waves computed at timelike worldtubes in the interior of a 3+1 (Cauchy) numerical relativity simulations. In our method, numerical relativity data are used as the inner inflowing boundary of a perturbative time-domain Regge-Wheeler-Zerilli simulation in hyperboloidal coordinates that reaches null infinity. We showcase waveforms from (3+1)D simulations of gravitational collapse of rotating neutron stars, binary black holes mergers and scattering, and binary neutron star mergers and compare them to other extrapolation methods. Our perturbative hyperboloidal extraction provides a simple yet efficient procedure to compute gravitational waves with data quality comparable to the Cauchy characteristic extraction for several practical applications. Nonlinear effects in the wave propagation are not captured by our method, but the present work is a stepping stone towards more sophisticated hyperboloidal schemes for gravitational-wave extraction.
We revisit the problem of gravitational-wave extraction in numerical relativity with gauge-invariant metric perturbation theory of spherical spacetimes. Our extraction algorithm allows the computation of even-parity (Zerilli-Moncrief) and odd-parity (Regge-Wheeler) multipoles of the strain from a (3+1) metric without the assumption that the spherical background is in Schwarzschild coordinates. The algorithm is validated with a comprehensive suite of 3D problems including fluid ($f$-modes) and spacetime ($w$-modes) perturbations of neutron stars, gravitational collapse of rotating neutron stars, circular binary black holes mergers and black hole dynamical captures and binary neutron star mergers. We find that metric extraction is robust in all the considered scenarios and delivers waveforms of overall quality similar to curvature (Weyl) extraction. Metric extraction is particularly valuable in identifying waveform systematics for problems in which the reconstruction of the strain from the Weyl multipoles is ambiguous. Direct comparison of different choices for the gauge-invariant master functions show very good agreement in the even-parity sector. Instead, in the odd-parity sector, assuming the background in Schwarzschild coordinates can minimize gauge effects related to the use of the $\Gamma$-driver shift. Moreover, for optimal choices of the extraction radius, a simple extrapolation to null infinity can deliver waveforms compatible to Cauchy-characteristic extrapolated waveforms.
In this project, we simulate the collision of two and three black holes using NRPy+ (`Python-based code generation for numerical relativity and beyond') module and BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation, and extract the resulting gravitational waveforms. Using Brill-Lindquist initial data and sixth-order finite differences, we evolve the system using the BSSN formulation and compute the gravitational-wave signal via the Weyl scalar $\psi_4$. To assess numerical error, we plot the Hamiltonian constraint and observe that constraint violations are significantly higher in the three-black-hole collision. Unexpected gravitational recoil is also detected, which may influence waveform extraction and that is left for further investigation. Despite the limitations in computational resources imposed by the Google Colab, we successfully model the merger of a binary black hole system, and we were able to extract the corresponding gravitational waves.
We present a new set of numerical-relativity simulations of merging binary neutron stars, aiming to identify possible observable signatures of the slope of the symmetry energy $L_{\rm sym}$. To achieve this goal, we employ a set of equations of state based on a parameterization of the covariant density functional theory of nuclear matter that allows controlled variations of $L_{\rm sym}$ and the skewness $Q_{\rm sat}$, holding the latter fixed. For a set of our simulations, we identify a steep energy gradient in the equation of state at subsaturation densities, which acts as a source of heating with subsequent stiffening produced by thermal support. Accounting for related structural modifications in the tidal deformability reconciles our results with theoretical expectations. On the other hand, we show that gravitational waves are unlikely to distinguish the role of $L_{\rm sym}$. In contrast to this, we find that the ejecta composition is significantly altered in our simulations, which employ an M1 moment scheme, when $L_{\rm sym}$ is varied. Based on our extracted dynamical ejecta properties, we compute r-process yields and find that they are distinct for the different $L_{\rm sym}$, especially at lower mass numbers $A \lesssim 120$. This suggests that electromagnetic counterparts are more likely to exhibit signatures; however, a direct connection to $L_{\rm sym}$ remains a challenge, given the complex interplay between details of the ejecta properties and the kilonova signal.
We have analyzed LVK gravitational wave events that show some evidence of eccentricity from TEOBResumS modeling parameter estimations and have confronted them independently with full numerical generated waveforms from our bank of nearly two thousand simulations of binary black holes. We have used RIFT for Bayesian parameter estimation and found that GW200208_{22} KDE estimates favor eccentricities $e_{20} = 0.217_{-0.184}^{+0.076}$ upon entering the LVK band at $\sim20$Hz within a 90% confidence limit. Within this event analysis we employed 39 new targeted full numerical relativity simulations and we have thus found a top improved likelihood $\ln \mathcal{L}$ matching waveform, compared to model-based analysis, with an estimated eccentricity at 20Hz, $e_{20}=0.200$, thus reinforcing the eccentric hypothesis of the binary. We have also used our full bank of numerical waveforms on GW190620 finding that it favors eccentricities in the range of {$0\leq e_{10}\leq0.3$}. New specifically targeted simulations will be required to narrow this eccentricity range.
We study the properties of remnants formed in prompt-collapse binary neutron star mergers. We consider non-spinning binaries over a range of total masses and mass ratios across a set of 22 equations of state, totaling 107 numerical relativity simulations. We report the final mass and spin of the systems (including the accretion disk and ejecta) to be constrained in a narrow range, regardless of the binary configuration and matter effects. This sets them apart from binary black-hole merger remnants. We assess the detectability of the postmerger signal in a future 40 km Cosmic Explorer observatory and find that the signal-to-noise ratio in the postmerger of an optimally located and oriented binary at a distance of 100 Mpc can range from ${<}1$ to 8, depending on the binary configuration and equation of state, with a majority of them greater than 4 in the set of simulations that we consider. We also consider the distinguishability between prompt-collapse binary neutron star and binary black hole mergers with the same masses and spins. We find that Cosmic Explorer will be able to distinguish such systems primarily via the measurement of tidal effects in the late inspiral. Neutron star binaries with reduced tidal deformability $\tilde\Lambda$ as small as ${\sim}3.5$ can be identified up to a distance of 100 Mpc, while neutron star binaries with $\tilde\Lambda\sim22$ can be identified to distances greater than 250 Mpc. This is larger than the distance up to which the postmerger will be visible. Finally, we discuss the possible implications of our findings for the equation of state of neutron stars from the gravitational-wave event GW230529.
We investigate the effects of large scalar inhomogeneities during the kination epoch, a period in which the universe's dynamics are dominated by the kinetic energy of a scalar field, by fully evolving the Einstein equations using numerical relativity. By tracking the non-linear growth of scalar perturbations with both sub-horizon and super-horizon initial wavelengths, we are able to compare their evolution to perturbative results. Our key findings show that in the deep sub-horizon limit, the perturbative behaviour remains valid, whereas in the super-horizon regime, non-linear dynamics exhibit a much richer phenomenology. Finally, we discuss the possibility of primordial black hole formation from the collapse of such perturbations and assess whether this process could serve as a viable mechanism to reheat the universe in the post-inflationary era.
Accurate and reliable gravitational waveform models are crucial in determining the properties of compact binary mergers. In particular, next-generation gravitational-wave detectors will require more accurate waveforms to avoid biases in the analysis. In this work, we extend the recent NRTidalv3 model to account for higher-mode corrections in the tidal phase contributions for binary neutron star systems. The higher-mode, multipolar NRTidalv3 model is then attached to several binary-black-hole baselines, such as the phenomenological IMRPhenomXHM and IMRPhenomXPHM models, and the effective-one-body-based model SEOBNRv5HM_ROM. We test the performance and validity of the newly developed models by comparing them with numerical-relativity simulations and other tidal models. Finally, we employ them in parameter estimation analyses on simulated signals from both comparable-mass and high-mass-ratio systems, as well as on the gravitational-wave event GW170817, for which we find consistent results with respect to previous analyses.