arXiv subjects

Denis Pollney

Publications and source records attributed to Denis Pollney.

At least 19 recordsLinked to original sources

arXiv2023

Numerical convergence of model Cauchy-characteristic extraction and matching

Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers. Cauchy-characteristic extraction and matching are methods to compute gravitational waves at null infinity, a mathematical idealization of detector location, from numerical relativity simulations. Both methods can in principle contribute to modeling by providing highly accurate gravitational waveforms. An underappreciated subtlety in realizing this potential is posed by the (mere) weak hyperbolicity of the particular PDE systems solved in the characteristic formulation of the Einstein field equations. This shortcoming results from the popular choice of Bondi-like coordinates. So motivated, we construct toy models that capture that PDE structure and study Cauchy-characteristic extraction and matching with them. Where possible we provide energy estimates for their solutions and perform careful numerical norm convergence tests to demonstrate the effect of weak hyperbolicity on Cauchy-characteristic extraction and matching. Our findings strongly indicate that, as currently formulated, Cauchy-characteristic matching for the Einstein field equations would provide solutions that are, at best, convergent at an order lower than expected for the numerical method, and may be unstable. In contrast, under certain conditions, the extraction method can provide properly convergent solutions. Establishing however that these conditions hold for the aforementioned characteristic formulations is still an open problem.

gr-qc↗

arXiv2023

Numerical solutions for the $f(R)$-Klein-Gordon system

We construct a numerical relativity code based on the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation for the gravitational quadratic $f(R)$ Starobinsky model. By removing the assumption that the determinant of the conformal 3-metric is unity, we first generalize the BSSN formulation for general $f(R)$ gravity theories in the metric formalism to accommodate arbitrary coordinates for the first time. We then describe the implementation of this formalism to the paradigmatic Starobinsky model. We apply the implementation to three scenarios: the Schwarzschild black hole solution, flat space with non-trivial gauge dynamics, and a massless Klein-Gordon scalar field. In each case, long-term stability and second-order convergence is demonstrated. The case of the massless Klein-Gordon scalar field is used to exercise the additional terms and variables resulting from the $f(R)$ contributions. For this model, we show for the first time that additional damped oscillations arise in the subcritical regime as the system approaches a stable configuration.

gr-qc↗

arXiv2021

Gauge structure of the Einstein field equations in Bondi-like coordinates

The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype formulations of this type are only weakly hyperbolic. Presently we examine the root cause of this result. In a linear analysis we identify the gauge, constraint and physical blocks in the principal part of the Einstein field equations in such a gauge, and show that the subsystem related to the gauge variables is only weakly hyperbolic. Weak hyperbolicity of the full system follows as a consequence in many cases. We demonstrate this explicitly in specific examples, and thus argue that Bondi-like gauges result in weakly hyperbolic free evolution systems under quite general conditions. Consequently the characteristic initial (boundary) value problem of GR in these gauges is rendered ill-posed in the simplest norms one would like to employ. The possibility of finding good alternative norms, in which well-posedness is achieved, is discussed. So motivated, we present numerical convergence tests with an implementation of full GR which demonstrate the effect of weak hyperbolicity in practice.

gr-qc↗

arXiv2015

Energetics and phasing of nonprecessing spinning coalescing black hole binaries

We present an improved numerical relativity (NR) calibration of the new effective-one-body (EOB) model for coalescing non precessing spinning black hole binaries recently introduced by Damour and Nagar [Physical Review D 90, 044018 (2014)]. We do so by comparing the EOB predictions to both the phasing and the energetics provided by two independent sets of NR data covering mass ratios $1\leq q \leq 9.989$ and dimensionless spin range $-0.95\leq \chi\leq +0.994$. One set of data is a subset of the Simulating eXtreme Spacetimes (SXS) catalog of public waveforms; the other set consists of new simulations obtained with the Llama code plus Cauchy Characteristic Evolution. We present the first systematic computation of the gauge-invariant relation between the binding energy and the total angular momentum, $E_{b}(j)$, for a large sample of, spin-aligned, SXS and Llama data. The dynamics of the EOB model presented here involves only two free functional parameters, one ($a_6^c(\nu)$) entering the non spinning sector, as a 5PN effective correction to the interaction potential, and one ($c_3(\tilde{a}_1,\tilde{a}_2,\nu))$ in the spinning sector, as an effective next-to-next-to-next-to-leading order correction to the spin-orbit coupling. These parameters are determined (together with a third functional parameter $\Delta t_{\rm NQC}(\chi)$ entering the waveform) by comparing the EOB phasing with the SXS phasing, the consistency of the energetics being checked afterwards. The quality of the analytical model for gravitational wave data analysis purposes is assessed by computing the EOB/NR faithfulness. Over the NR data sample and when varying the total mass between 20 and 200~$M_\odot$ the EOB/NR unfaithfulness (integrated over the NR frequency range) is found to vary between $99.493\%$ and $99.984\%$ with a median value of $99.944\%$.

gr-qc↗

arXiv2013

Evolution of linear perturbations in spherically symmetric dust spacetimes

We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate several configurations of physical interest, such as relativistic corrections to structure formation, the lensing of gravitational waves and the evolution of perturbations in a cosmological void model. This paper focuses on the latter problem, i.e. structure formation in a Hubble scale void in the linear regime. This is considerably more complicated than linear perturbations of a homogeneous and isotropic background because the inhomogeneous background leads to coupling between density perturbations and rotational modes of the spacetime geometry, as well as gravitational waves. Previous analyses of this problem ignored this coupling in the hope that the approximation does not affect the overall dynamics of structure formation in such models. We show that for a giga-parsec void, the evolution of the density contrast is well approximated by the previously studied decoupled evolution only for very large-scale modes. However, the evolution of the gravitational potentials within the void is inaccurate at more than the $10\%$ level, and is even worse on small scales.

astro-ph.CO↗

arXiv2013

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.

gr-qc↗

arXiv2012

General relativistic null-cone evolutions with a high-order scheme

We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. The scheme can offer significantly more accuracy with relatively low computational cost compared to previous methods as a result of the higher-order discretization. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.

gr-qc↗

arXiv2012

The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations.

gr-qc↗

arXiv2011

Energy versus Angular Momentum in Black Hole Binaries

Using accurate numerical relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1 and 3:1 we compute the gauge invariant relation between the (reduced) binding energy $E$ and the (reduced) angular momentum $j$ of the system. We show that the relation $E(j)$ is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity $E^{\rm NR} (j)$ curve with the predictions of several analytic approximation schemes, we find that, while the usual, non-resummed post-Newtonian-expanded $E^{\rm PN} (j)$ relation exhibits large and growing deviations from $E^{\rm NR} (j)$, the prediction of the effective one-body formalism, based purely on known analytical results (without any calibration to numerical relativity), agrees strikingly well with the numerical-relativity results.

gr-qc↗

arXiv2011

Initial data transients in binary black hole evolutions

We describe a method for initializing characteristic evolutions of the Einstein equations using a linearized solution corresponding to purely outgoing radiation. This allows for a more consistent application of the characteristic (null cone) techniques for invariantly determining the gravitational radiation content of numerical simulations. In addition, we are able to identify the {\em ingoing} radiation contained in the characteristic initial data, as well as in the initial data of the 3+1 simulation. We find that each component leads to a small but long lasting (several hundred mass scales) transient in the measured outgoing gravitational waves.

gr-qc↗

arXiv2010

Notes on the integration of numerical relativity waveforms

A primary goal of numerical relativity is to provide estimates of the wave strain, $h$, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, $\psi_4$. Assuming Bondi gauge, transforming to the strain $h$ reduces to integration of $\psi_4$ twice in time. Integrations performed in either the time or frequency domain, however, lead to secular non-linear drifts in the resulting strain $h$. These non-linear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular non-linear drifts in the resulting strain.

gr-qc↗

arXiv2010

Gravitational memory in binary black hole mergers

In addition to the dominant oscillatory gravitational wave signals produced during binary inspirals, a non-oscillatory component arises from the nonlinear "memory" effect, sourced by the emitted gravitational radiation. The memory grows significantly during the late inspiral and merger, modifying the signal by an almost step-function profile, and making it difficult to model by approximate methods. We use numerical evolutions of binary black holes to evaluate the nonlinear memory during late-inspiral, merger and ringdown. We identify two main components of the signal: the monotonically growing portion corresponding to the memory, and an oscillatory part which sets in roughly at the time of merger and is due to the black hole ringdown. Counter-intuitively, the ringdown is most prominent for models with the lowest total spin. Thus, the case of maximally spinning black holes anti-aligned to the orbital angular momentum exhibits the highest signal-to-noise (SNR) for interferometric detectors. The largest memory offset, however, occurs for highly spinning black holes, with an estimated value of h^tot_20 \approx 0.24 in the maximally spinning case. These results are central to determining the detectability of nonlinear memory through pulsar timing array measurements.

gr-qc↗

arXiv2009

Vacuum Electromagnetic Counterparts of Binary Black-Hole Mergers

As one step towards a systematic modeling of the electromagnetic (EM) emission from an inspiralling black hole binary we consider a simple scenario in which the binary moves in a uniform magnetic field anchored to a distant circumbinary disc. We study this system by solving the Einstein-Maxwell equations in which the EM fields are chosen with astrophysically consistent strengths. We consider binaries with spins aligned or anti-aligned with the orbital angular momentum and study the dependence of gravitational and EM signals with these spin configurations. Overall we find that the EM radiation in the lowest l=2, m=2 multipole accurately reflects the gravitational one, with identical phase evolutions and amplitudes that differ only by a scaling factor. We also compute the efficiency of the energy emission in EM waves and find that it is given by E^rad_EM/M ~ 10^-15 (M/10^8 M_Sun)^2 (B/10^4 G)^2, hence 13 orders of magnitude smaller than the gravitational energy for realistic magnetic fields. The corresponding luminosity is much smaller than the accretion luminosity if the system is accreting at near the Eddington rate. Most importantly, this EM emission is at frequencies of 10^-4 (10^8 M_Sun/M) Hz, well outside those accessible to astronomical radio observations. As a result, it is unlikely that the EM emission discussed here can be detected directly and simultaneously with the gravitational-wave one. However, indirect processes, driven by changes in the EM fields behavior could yield observable events. In particular if the accretion rate of the circumbinary disc is small and sufficiently stable over the timescale of the final inspiral, then the EM emission may be observable indirectly as it will alter the accretion rate through the magnetic torques exerted by the distorted magnetic field lines.

gr-qc↗

arXiv2009

High accuracy binary black hole simulations with an extended wave zone

We present results from a new code for binary black hole evolutions using the moving-puncture approach, implementing finite differences in generalised coordinates, and allowing the spacetime to be covered with multiple communicating non-singular coordinate patches. Here we consider a regular Cartesian near zone, with adapted spherical grids covering the wave zone. The efficiencies resulting from the use of adapted coordinates allow us to maintain sufficient grid resolution to an artificial outer boundary location which is causally disconnected from the measurement. For the well-studied test-case of the inspiral of an equal-mass non-spinning binary (evolved for more than 8 orbits before merger), we determine the phase and amplitude to numerical accuracies better than 0.010% and 0.090% during inspiral, respectively, and 0.003% and 0.153% during merger. The waveforms, including the resolved higher harmonics, are convergent and can be consistently extrapolated to $r\to\infty$ throughout the simulation, including the merger and ringdown. Ringdown frequencies for these modes (to $(\ell,m)=(6,6)$) match perturbative calculations to within 0.01%, providing a strong confirmation that the remnant settles to a Kerr black hole with irreducible mass $M_{\rm irr} = 0.884355\pm20\times10^{-6}$ and spin $S_f/M_f^2 = 0.686923 \pm 10\times10^{-6}$

gr-qc↗

arXiv2009

The Asymptotic Falloff of Local Waveform Measurements in Numerical Relativity

We examine current numerical relativity computations of gravitational waves, which typically determine the asymptotic waves at infinity by extrapolation from finite (small) radii. Using simulations of a black hole binary with accurate wave extraction at $r=1000M$, we show that extrapolations from the near-zone are self-consistent in approximating measurements at this radius, although with a somewhat reduced accuracy. We verify that $\psi_4$ is the dominant asymptotic contribution to the gravitational energy (as required by the peeling theorem) but point out that gauge effects may complicate the interpretation of the other Weyl components.

gr-qc↗

arXiv2009

Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins

Binary black-hole systems with spins aligned or anti-aligned to the orbital angular momentum provide the natural ground to start detailed studies of the influence of strong-field spin effects on gravitational wave observations of coalescing binaries. Furthermore, such systems may be the preferred end-state of the inspiral of generic supermassive binary black-hole systems. In view of this, we have computed the inspiral and merger of a large set of binary systems of equal-mass black holes with spins parallel to the orbital angular momentum but otherwise arbitrary. Our attention is particularly focused on the gravitational-wave emission so as to quantify how much spin effects contribute to the signal-to-noise ratio, to the horizon distances, and to the relative event rates for the representative ranges in masses and detectors. As expected, the signal-to-noise ratio increases with the projection of the total black hole spin in the direction of the orbital momentum. We find that equal-spin binaries with maximum spin aligned with the orbital angular momentum are more than "three times as loud" as the corresponding binaries with anti-aligned spins, thus corresponding to event rates up to 30 times larger. We also consider the waveform mismatch between the different spinning configurations and find that, within our numerical accuracy, binaries with opposite spins S_1=-S_2 cannot be distinguished whereas binaries with spin S_1=S_2 have clearly distinct gravitational-wave emissions. Finally, we derive a simple expression for the energy radiated in gravitational waves and find that the binaries always have efficiencies E_rad/M > 3.6%, which can become as large as E_rad/M = 10% for maximally spinning binaries with spins aligned with the orbital angular momentum.

gr-qc↗

arXiv2009

Status of NINJA: the Numerical INJection Analysis project

The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise.

gr-qc↗

arXiv2009

Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the Initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter-estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

gr-qc↗