arXiv subjects

Nils L. Vu

Publications and source records attributed to Nils L. Vu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Modeling the BMS transformation induced by a binary black hole merger

Understanding the characteristics of the remnant black hole formed in a binary black hole merger is crucial for conducting gravitational wave astronomy. Typically, models of remnant black holes provide information about their mass, spin, and kick velocity. However, other information related to the supertranslation symmetries of the BMS group, such as the memory effect, is also important for characterizing the final state of the system. In this work, we build a model of the BMS transformation that maps a binary black hole's inspiral frame to the remnant black hole's canonical rest frame. Training data for this model are created using high-precision numerical relativity simulations of quasi-circular systems with mass ratios $q \le 8$ and spins parallel to the orbital angular momentum with magnitudes $χ_{1}, χ_{2} \le 0.8$. We use Gaussian Process Regression to model the BMS transformations over the three-dimensional parameter space $\left(q, χ_{1}^{z}, χ_{2}^{z}\right)$. The physics captured by this model is strictly non-perturbative and cannot be obtained from post-Newtonian approximations alone, as it requires knowledge of the strong nonlinear effects that are sourced during the merger. Apart from providing the first model of the supertranslation induced by a binary black hole merger, we also find that the kick velocities predicted using Cauchy-characteristic evolution waveforms are, on average, $\sim5\%$ larger than the ones obtained from extrapolated waveforms. Our work has broad implications for improving gravitational wave models and studying the large-scale impact of memory, such as on the cosmological background. The fits produced in this work are available through the Python package $\texttt{surfinBH}$ under the name $\texttt{NRSur3dq8BMSRemnant}$.

gr-qc↗

arXiv2025

Black Hole Spectroscopy for Precessing Binary Black Hole Coalescences

The spectroscopic study of black hole quasinormal modes in gravitational-wave ringdown observations is hindered by our ignorance of which modes should dominate astrophysical signals for different binary configurations, limiting tests of general relativity and astrophysics. In this work, we present a description of the quasinormal modes that are excited in the ringdowns of comparable mass, quasi-circular precessing binary black hole coalescences -- a key region of parameter space that has yet to be fully explored within the framework of black hole spectroscopy. We suggest that the remnant perturbation for precessing and non-precessing systems is approximately the same up to a rotation, which implies that the relative amplitudes of the quasinormal modes in both systems are also related by a rotation. We present evidence for this by analyzing an extensive catalog of numerical relativity simulations. Additional structure in the amplitudes is connected to the system's kick velocity and other asymmetries in the orbital dynamics. We find that the ringdowns of precessing systems need not be dominated by the ${(\ell,m)=(2,\pm 2)}$ quasinormal modes, and that instead the $(2,\pm 1)$~or~$(2,0)$ quasinormal modes can dominate. Our results are consistent with a ringdown analysis of the LIGO-Virgo gravitational wave signal GW190521, and may also help in understanding phenomenological inspiral-merger-ringdown waveform model systematics.

gr-qc↗

arXiv2025

Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity

Recent efforts to numerically simulate compact objects in alternative theories of gravity have largely focused on the time-evolution equations. Another critical aspect is the construction of constraint-satisfying initial data with precise control over the properties of the systems under consideration. Here, we augment the extended conformal thin sandwich framework to construct quasistationary initial data for black hole systems in scalar Gauss-Bonnet theory and numerically implement it in the open-source SpECTRE code. Despite the resulting elliptic system being singular at black hole horizons, we demonstrate how to construct numerical solutions that extend smoothly across the horizon. We obtain quasistationary scalar hair configurations in the test-field limit for black holes with linear/angular momentum as well as for black hole binaries. For isolated black holes, we explicitly show that the scalar profile obtained is stationary by evolving the system in time and compare against previous formulations of scalar Gauss-Bonnet initial data. In the case of the binary, we find that the scalar hair near the black holes can be markedly altered by the presence of the other black hole. The initial data constructed here enable targeted simulations in scalar Gauss-Bonnet simulations with reduced initial transients.

gr-qc↗

arXiv2025

Einstein-Klein-Gordon system via Cauchy-characteristic evolution: Computation of memory and ringdown tail

Cauchy-characteristic evolution (CCE) is a powerful method for accurately extracting gravitational waves at future null infinity. In this work, we extend the previously implemented CCE system within the numerical relativity code SpECTRE by incorporating a scalar field. This allows the system to capture features of beyond-general-relativity theories. We derive scalar contributions to the equations of motion, Weyl scalar computations, Bianchi identities, and balance laws at future null infinity. Our algorithm, tested across various scenarios, accurately reveals memory effects induced by both scalar and tensor fields and captures Price's power-law tail ($u^{-l-2}$) in scalar fields at future null infinity, in contrast to the $t^{-2l-3}$ tail at future timelike infinity.

gr-qc↗

arXiv2025

Simulating binary black hole mergers using discontinuous Galerkin methods

Binary black holes are the most abundant source of gravitational-wave observations. Gravitational-wave observatories in the next decade will require tremendous increases in the accuracy of numerical waveforms modeling binary black holes, compared to today's state of the art. One approach to achieving the required accuracy is using spectral-type methods that scale to many processors. Using the SpECTRE numerical-relativity code, we present the first simulations of a binary black hole inspiral, merger, and ringdown using discontinuous Galerkin methods. The efficiency of discontinuous Galerkin methods allows us to evolve the binary through ~18 orbits at reasonable computational cost. We then use SpECTRE's Cauchy Characteristic Evolution (CCE) code to extract the gravitational waves at future null infinity. The open-source nature of SpECTRE means this is the first time a spectral-type method for simulating binary black hole evolutions is available to the entire numerical-relativity community.

gr-qc↗

arXiv2024

Late-time tails in nonlinear evolutions of merging black holes

We uncover late-time gravitational-wave tails in fully nonlinear 3+1 dimensional numerical relativity simulations of merging black holes, using the highly accurate SpEC code. We achieve this result by exploiting the strong magnification of late-time tails due to binary eccentricity, recently observed in perturbative evolutions, and showcase here the tail presence in head-on configurations for several mass ratios close to unity. We validate the result through a large battery of numerical tests and detailed comparison with perturbative evolutions, which display striking agreement with full nonlinear ones. Our results offer yet another confirmation of the highly predictive power of black hole perturbation theory in the presence of a source, even when applied to nonlinear solutions. The late-time tail signal is much more prominent than anticipated until recently, and possibly within reach of gravitational-wave detectors measurements, unlocking observational investigations of an additional set of general relativistic predictions on the long-range gravitational dynamics.

gr-qc↗

arXiv2024

A Review of Gravitational Memory and BMS Frame Fixing in Numerical Relativity

Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our universe.

gr-qc↗

arXiv2024

Discontinuous Galerkin scheme for elliptic equations on extremely stretched grids

Discontinuous Galerkin (DG) methods for solving elliptic equations are gaining popularity in the computational physics community for their high-order spectral convergence and their potential for parallelization on computing clusters. However, problems in numerical relativity with extremely stretched grids, such as initial data problems for binary black holes that impose boundary conditions at large distances from the black holes, have proven challenging for DG methods. To alleviate this problem we have developed a primal DG scheme that is generically applicable to a large class of elliptic equations, including problems on curved and extremely stretched grids. The DG scheme accommodates two widely used initial data formulations in numerical relativity, namely the puncture formulation and the extended conformal thin-sandwich (XCTS) formulation. We find that our DG scheme is able to stretch the grid by a factor of $\sim 10^9$ and hence allows to impose boundary conditions at large distances. The scheme converges exponentially with resolution both for the smooth XCTS problem and for the nonsmooth puncture problem. With this method we are able to generate high-quality initial data for binary black hole problems using a parallelizable DG scheme. The code is publicly available in the open-source SpECTRE numerical relativity code.

gr-qc↗

arXiv2024

Binary neutron star mergers using a discontinuous Galerkin-finite difference hybrid method

We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-Characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods.

gr-qc↗

arXiv2024

High-Precision Ringdown Surrogate Model for Non-Precessing Binary Black Holes

Highly precise and robust waveform models are required as improvements in detector sensitivity enable us to test general relativity with more precision than ever before. In this work, we introduce a spin-aligned surrogate ringdown model. This ringdown surrogate, NRSur3dq8_RD, is built with numerical waveforms produced using Cauchy-characteristic evolution. In addition, these waveforms are in the superrest frame of the remnant black hole allowing us to do a correct analysis of the ringdown spectrum. The novel prediction of our surrogate model is complex-valued quasinormal mode (QNM) amplitudes, with median relative errors of $10^{-2}-10^{-3}$ over the parameter space. Like previous remnant surrogates, we also predict the remnant black hole's mass and spin. The QNM mode amplitude errors translate into median errors on ringdown waveforms of $10^{-4}$. The high accuracy and QNM mode content provided by our surrogate will enable high-precision ringdown analyses such as tests of general relativity. Our ringdown model is publicly available through the python package surfinBH.

gr-qc↗

arXiv2024

Striking the right tone: toward a self-consistent framework for measuring black hole ringdowns

The ringdown portion of a binary black hole merger consists of a sum of modes, each containing an infinite number of tones that are exponentially damped sinusoids. In principle, these can be measured as gravitational-waves with observatories like LIGO/Virgo/KAGRA, however in practice it is unclear how many tones can be meaningfully resolved. We investigate the consistency and resolvability of the overtones of the quadrupolar $\ell = m = 2$ mode by starting at late times when the gravitational waveform is expected to be well-approximated by the $\ell m n = 220$ tone alone. We present a Bayesian inference framework to measure the tones in numerical relativity data. We measure tones at different start times, checking for consistency: we classify a tone as stably recovered if and only if the 95\% credible intervals for amplitude and phase at time $t$ overlap with the credible intervals at all subsequent times. We test a set of tones including the first four overtones of the fundamental mode and the 320 tone and find that the 220 and 221 tones can be measured consistently with the inclusion of additional overtones. The 222 tone measurements can be stabilised when we include the 223 tone, but only in a narrow time window, after which it is too weak to measure. The 223 tone recovery appears to be unstable, and does not become stable with the introduction of the 224 tone. We find that $N=3$ tones can be stably recovered simultaneously. However, when analysing $N \geq 4$ tones, the amplitude of one tone is consistent with zero. Thus, within our framework, one can identify only $N=3$ tones with non-zero amplitude that are simultaneously stable.

gr-qc↗

arXiv2024

Fully relativistic three-dimensional Cauchy-characteristic matching for physical degrees of freedom

A fully relativistic three-dimensional Cauchy-characteristic matching (CCM) algorithm is implemented for physical degrees of freedom in a numerical relativity code SpECTRE. The method is free of approximations and can be applied to any physical system. We test the algorithm with various scenarios involving smooth data, including the propagation of Teukolsky waves within a flat background, the perturbation of a Kerr black hole with a Teukolsky wave, and the injection of a gravitational-wave pulse from the characteristic grid. Our investigations reveal no numerical instabilities in the simulations. In addition, the tests indicate that the CCM algorithm effectively directs characteristic information into the inner Cauchy system, yielding higher precision in waveforms and smaller violations of Bondi-gauge constraints, especially when the outer boundary of the Cauchy evolution is at a smaller radius.

gr-qc↗

arXiv2024

Improved frequency spectra of gravitational waves with memory in a binary-black-hole simulation

Numerical relativists can now produce gravitational waveforms with memory effects routinely and accurately. The gravitational-wave memory effect contains very low-frequency components, including a persistent offset. The presence of these components violates basic assumptions about time-shift behavior underpinning standard data-analysis techniques in gravitational-wave astronomy. This poses a challenge to the analysis of waveform spectra: How to preserve the low-frequency characteristics when transforming a time-domain waveform to the frequency domain. To tackle this challenge, we revisit the preprocessing procedures applied to the waveforms that contain memory effects. We find inconsistency between the zero-frequency limit of displacement memory and the low- frequency spectrum of the same memory preprocessed using the common scheme in literature. To resolve the inconsistency, we propose a new robust preprocessing scheme that produces the spectra of memory waveforms more faithfully. Using this new scheme, we inspect several characteristics of the spectrum of a memory waveform. In particular, we find a discernible beating pattern formed by the dominant oscillatory mode and the displacement memory. This pattern is absent in the spectrum of a waveform without memory. The difference between the memory and no-memory waveforms is too small to be observed by current-generation detectors in a single binary-black-hole event. Detecting the memory in a single event is likely to occur in the era of next-generation detectors.

gr-qc↗

arXiv2024

Scalarization of isolated black holes in scalar Gauss-Bonnet theory in the fixing-the-equations approach

One of the most promising avenues to perform numerical evolutions in theories beyond General Relativity is the fixing-the-equations approach, a proposal in which new ``driver'' equations are added to the evolution equations in a way that allows for stable numerical evolutions. In this direction, we extend the numerical relativity code SpECTRE to evolve a ``fixed'' version of scalar Gauss-Bonnet theory in the decoupling limit, a phenomenologically interesting theory that allows for hairy black hole solutions in vacuum. We focus on isolated black hole systems both with and without linear and angular momentum, and propose a new driver equation to improve the recovery of such stationary solutions. We demonstrate the effectiveness of the latter by numerically evolving black holes that undergo spontaneous scalarization using different driver equations. Finally, we evaluate the accuracy of the obtained solutions by comparing with the original unaltered theory.

gr-qc↗

arXiv2024

Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field model in 3+1 dimensions

Binary black hole simulations become increasingly more computationally expensive with smaller mass ratios, partly because of the longer evolution time, and partly because the lengthscale disparity dictates smaller time steps. The program initiated by Dhesi et al. (arXiv:2109.03531) explores a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range ($10^{-4} \lesssim q \lesssim 10^{-2}$), where purely perturbative methods may not be adequate. A region ("worldtube") much larger than the small black hole is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. Here we apply this idea to a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field. This is a first implementation of the worldtube excision method in full 3+1 dimensions. We demonstrate the accuracy and efficiency of the method, and discuss the steps towards applying it for evolving orbits and, ultimately, in the binary black-hole scenario. Our implementation is publicly accessible in the SpECTRE numerical relativity code.

gr-qc↗

arXiv2024

A positivity-preserving adaptive-order finite-difference scheme for GRMHD

We present an adaptive-order positivity-preserving conservative finite-difference scheme that allows a high-order solution away from shocks and discontinuities while guaranteeing positivity and robustness at discontinuities. This is achieved by monitoring the relative power in the highest mode of the reconstructed polynomial and reducing the order when the polynomial series no longer converges. Our approach is similar to the multidimensional optimal order detection (MOOD) strategy, but differs in several ways. The approach is a priori and so does not require retaking a time step. It can also readily be combined with positivity-preserving flux limiters that have gained significant traction in computational astrophysics and numerical relativity. This combination ultimately guarantees a physical solution both during reconstruction and time stepping. We demonstrate the capabilities of the method using a standard suite of very challenging 1d, 2d, and 3d general relativistic magnetohydrodynamics test problems.

astro-ph.HE↗

arXiv2024

Nonlinear Effects In Black Hole Ringdown From Scattering Experiments I: spin and initial data dependence of quadratic mode coupling

We investigate quadratic quasinormal mode coupling in black hole spacetime through numerical simulations of single perturbed black holes using both numerical relativity and second-order black hole perturbation theory. Focusing on the dominant $\ell=|m|=2$ quadrupolar modes, we find good agreement (within $\sim10\%$) between these approaches, with discrepancies attributed to truncation error and uncertainties from mode fitting. Our results align with earlier studies extracting the coupling coefficients from select binary black hole merger simulations, showing consistency for the same remnant spins. Notably, the coupling coefficient is insensitive to a diverse range of initial data, including configurations that led to a significant (up to $5\%$) increase in the remnant black hole mass. These findings present opportunities for testing the nonlinear dynamics of general relativity with ground-based gravitational wave observatories. Lastly, we provide evidence of a bifurcation in coupling coefficients between counter-rotating and co-rotating quasinormal modes as black hole spin increases.

gr-qc↗

arXiv2023

Extending black-hole remnant surrogate models to extreme mass ratios

Numerical-relativity surrogate models for both black-hole merger waveforms and remnants have emerged as important tools in gravitational-wave astronomy. While producing very accurate predictions, their applicability is limited to the region of the parameter space where numerical-relativity simulations are available and computationally feasible. Notably, this excludes extreme mass ratios. We present a machine-learning approach to extend the validity of existing and future numerical-relativity surrogate models toward the test-particle limit, targeting in particular the mass and spin of post-merger black-hole remnants. Our model is trained on both numerical-relativity simulations at comparable masses and analytical predictions at extreme mass ratios. We extend the gaussian-process-regression model NRSur7dq4Remnant, validate its performance via cross validation, and test its accuracy against additional numerical-relativity runs. Our fit, which we dub NRSur7dq4EmriRemnant, reaches an accuracy that is comparable to or higher than that of existing remnant models while providing robust predictions for arbitrary mass ratios.

gr-qc↗