Table of contents

This special issue of Classical and Quantum Gravity contains articles submitted in relation to the 'Theory Meets Data Analysis at Comparable and Extreme Mass Ratios' conference held at the Perimeter Institute for Theoretical Physics, Waterloo, Canada, 20–26 June 2010. This conference, organized by S Fairhurst, G Gonzalez, L Lehner, Y Liu, H Pfeiffer, and E Poisson brought together researchers from three gravitational wave communities: experiment, theory and data analysis, who discussed the latest advances and challenges for detecting and exploiting gravitational waves.

Approximately 60 talks spread over one week, together with many lively discussions provided an excellent atmosphere for debate. With so much packed in over seven days there were too many highlights to list specifics here. However, several common themes could be clearly discerned: the tremendous progress achieved in the detector level; the understanding of key comparable-mass systems and the data analysis techniques required for searching for their signals; the significant progress achieved in obtaining predictions in extreme mass ratio scenarios and the understanding of remaining challenges; as well as several new efforts towards making multi-messenger astronomy a reality. This issue contains research articles presented at this conference which, together with online talks (all of which can be found at pirsa.org/C10015), illustrate the level of maturity the field has reached. Many challenges still remain and the communities involved are actively working towards addressing them.

The advent of long-term stability in numerical relativity has yielded a windfall of answers to long-standing questions regarding the dynamics of space-time, matter, and electromagnetic fields in the strong-field regime of black-hole binary mergers. In this review, we will briefly summarize the methodology currently applied to these problems, emphasizing the most recent advancements. We will discuss recent results of astrophysical relevance, and present some novel interpretation. Although we primarily present a review, we also present a simple analytical model for the time-dependent Poynting flux from two orbiting black holes immersed in a magnetic field, which compares favorably with recent numerical results. Finally, we will discuss recent advancements in our theoretical understanding of merger dynamics and gravitational waveforms that have resulted from interpreting the ever-growing body of numerical relativity results.

This paper presents a study of the sufficient accuracy of post-Newtonian and numerical relativity waveforms for the most demanding usage case: parameter estimation of strong sources in advanced gravitational wave detectors. For black hole binaries, these detectors require accurate waveform models which can be constructed by fusing an analytical post-Newtonian inspiral waveform with a numerical relativity merger-ringdown waveform. We perform a comprehensive analysis of errors that enter such 'hybrid waveforms'. We find that the post-Newtonian waveform must be aligned with the numerical relativity waveform to exquisite accuracy, about 1/100 of a gravitational wave cycle. Phase errors in the inspiral phase of the numerical relativity simulation must be controlled to ≲  0.1 rad. (These numbers apply to moderately optimistic estimates about the number of GW sources; exceptionally strong signals require even smaller errors.) The dominant source of error arises from the inaccuracy of the investigated post-Newtonian Taylor approximants. Using our error criterion, even at 3.5th post-Newtonian order, hybridization has to be performed significantly before the start of the longest currently available numerical waveforms which cover 30 gravitational wave cycles. The current investigation is limited to the equal-mass, zero-spin case and does not take into account calibration errors of the gravitational wave detectors.

Traditional black-hole (BH) binary puncture initial data is conformally flat. This unphysical assumption is coupled with a lack of radiation signature from the binary's past life. As a result, waveforms extracted from evolutions of this data display an abrupt jump. In Kelly et al (2010, Class. Quantum Grav.27 114005), a new binary BH initial data with radiation content derived from post-Newtonian (PN) theory was adapted to puncture evolutions in numerical relativity. This data satisfies the constraint equations to the 2.5PN order, and contains a transverse-traceless 'wavy' metric contribution, violating the standard assumption of conformal flatness. Although the evolution contained less spurious radiation, there were undesirable features: unphysical horizon mass loss and large initial orbital eccentricity. Introducing a hybrid approach to the initial data evaluation, we significantly reduce these undesired features.

We analyse an 11-orbit inspiral of a non-spinning black-hole binary with mass ratio q ≡ M₁/M₂ = 4. The numerically obtained gravitational waveforms are compared with post-Newtonian (PN) predictions including several subdominant multipoles up to multipolar indices (l = 5, m = 5). We find that (i) numerical and post-Newtonian predictions of the phase of the (2, 2) mode accumulate a phase difference of about 0.35 rad at the PN cut-off frequency Mω = 0.1 for the Taylor T1 approximant when numerical and PN waveforms are matched over a window in the early inspiral phase; (ii) in contrast to previous studies of equal mass and specific spinning binaries, we find the Taylor T4 approximant to agree less well with numerical results, provided the latter are extrapolated to infinite extraction radius; (iii) extrapolation of gravitational waveforms to infinite extraction radius is particularly important for subdominant multipoles with l ≠ m; (iv) 3PN terms in post-Newtonian multipole expansions significantly improve the agreement with numerical predictions for subdominant multipoles.

Recently, we proposed an enhancement of the Regge–Wheeler–Zerilli formalism for first-order perturbations about a Schwarzschild background that includes first-order corrections due to the background black-hole spin in the black-hole perturbation approach. Using this formalism, we analytically investigate gravitational wave emission and linear momentum flux from a head-on collision of two spinning black holes in the extreme mass-ratio limit. The result derived in the lowest slow-motion and weak-field approximations here is consistent with the post-Newtonian calculation.

In this paper, we present a work in progress toward an efficient and economical computational module which interfaces between Cauchy and characteristic evolution codes. Our goal is to provide a standardized waveform extraction tool for the numerical relativity community which will allow CCE to be readily applied to a generic Cauchy code. The tool provides a means of unambiguous comparison between the waveforms generated by evolution codes based upon different formulations of the Einstein equations and different numerical approximation.

The Blandford–Znajek (BZ) mechanism has long been regarded as a key ingredient in models attempting to explain powerful jets in AGNs, quasars, blazzars, etc. In such a mechanism, energy is extracted from a rotating black hole and dissipated at a load at far distances. In this work we examine the behavior of the BZ mechanism with respect to different boundary conditions, revealing the robustness of the mechanism upon variation of these conditions. Consequently, this work closes a gap in our understanding of this important scenario.

In this paper, we present a method for conducting a coherent search for single-spin compact binary coalescences in gravitational wave data and compare this search to the existing coincidence method for single-spin searches. We propose a method to characterize the regions of the parameter space where the single-spin search, both coincident and coherent, will increase detection efficiency over the existing non-precessing search. We also show example results of the coherent search on a stretch of data from Laser Interferometer Gravitational-wave Observatory's fourth science run, but note that a set of signal-based vetoes will be needed before this search can be run to try to make detections.

We describe a hierarchical data analysis pipeline for coherently searching for gravitational-wave signals from non-spinning compact binary coalescences (CBCs) in the data of multiple earth-based detectors. This search assumes no prior information on the sky position of the source or the time of occurrence of its transient signals and, hence, is termed 'blind'. The pipeline computes the coherent network search statistic that is optimal in stationary, Gaussian noise. More importantly, it allows for the computation of a suite of alternative multi-detector coherent search statistics and signal-based discriminators that can improve the performance of CBC searches in real data, which can be both non-stationary and non-Gaussian. Also, unlike the coincident multi-detector search statistics that have been employed so far, the coherent statistics are different in the sense that they check for the consistency of the signal amplitudes and phases in the different detectors with their different orientations and with the signal arrival times in them. Since the computation of coherent statistics entails searching in the sky, it is more expensive than that of the coincident statistics that do not require it. To reduce computational costs, the first stage of the hierarchical pipeline constructs coincidences of triggers from the multiple interferometers, by requiring their proximity in time and component masses. The second stage follows up on these coincident triggers by computing the coherent statistics. Here, we compare the performances of this hierarchical pipeline with and without the second (or coherent) stage in Gaussian noise. Although introducing hierarchy can be expected to cause some degradation in the detection efficiency compared to that of a single-stage coherent pipeline, nevertheless it improves the computational speed of the search considerably. The two main results of this work are as follows: (1) the performance of the hierarchical coherent pipeline on Gaussian data is shown to be better than the pipeline with just the coincident stage; (2) the three-site network of LIGO detectors, in Hanford and Livingston (USA), and Virgo detector in Cascina (Italy) cannot resolve the polarization of waves arriving from certain parts of the sky. This can cause the three-site coherent statistic at those sky positions to become singular. Regularized versions of the statistic can avoid that problem, but can be expected to be sub-optimal. The aforementioned improvement in the pipeline's performance due to the coherent stage is in spite of this handicap.

Numerical evaluation of the self-force on a point particle is made difficult by the use of delta functions as sources. Recent methods for self-force calculations avoid delta functions altogether, using instead a finite and extended 'effective source' for a point particle. We provide a review of the general principles underlying this strategy, using the specific example of a scalar point charge moving in a black hole spacetime. We also report on two new developments: (i) the construction and evaluation of an effective source for a scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii) the successful implementation of hyperboloidal slicing that significantly improves on previous treatments of boundary conditions used for effective-source-based self-force calculations. Finally, we identify some of the key issues related to the effective source approach that will need to be addressed by future work.

The computation of the self-force constitutes one of the main challenges for the construction of precise theoretical waveform templates in order to detect and analyze extreme-mass-ratio inspirals with the future space-based gravitational-wave observatory LISA. Since the number of templates required is quite high, it is important to develop fast algorithms both for the computation of the self-force and the production of waveforms. In this paper, we show how to tune a recent time-domain technique for the computation of the self-force, what we call the particle without particle scheme, in order to make it very precise and at the same time very efficient. We also extend this technique in order to allow for highly eccentric orbits.

On the basis of a recently proposed strategy of finite element integration in time domain for partial differential equations with a singular source term, we present a fourth-order algorithm for non-rotating black hole perturbations in the Regge–Wheeler gauge. Herein, we address even perturbations induced by a particle plunging in. The forward time value at the upper node of the (r*, t) grid cell is obtained by an algebraic sum of (i) the preceding node values of the same cell, (ii) analytic expressions, related to the jump conditions on the wavefunction and its derivatives and (iii) the values of the wavefunction at adjacent cells. In this approach, the numerical integration does not deal with the source and potential terms directly, for cells crossed by the particle world line. This scheme has also been applied to circular and eccentric orbits and it will be the object of a forthcoming publication.