by Hannam, Mark and Husa, Sascha and Ohme, Frank and Mueller, Doreen and Bruegmann, Bernd
20 pages, 9 figures, 6 tables

We present gravitational waveforms for the last orbits and merger of black-hole-binary (BBH) systems along two branches of the BBH parameter space: equal-mass binaries with equal non-precessing spins, and nonspinning unequal-mass binaries. The waveforms are calculated from numerical solutions of Einstein’s equations for black-hole binaries that complete between six and ten orbits before merger. Along the equal-mass spinning branch, the spin parameter of each BH is $latex \chi_i = S_i/M_i^2 \in [-0.85,0.85]$, and along the unequal-mass branch the mass ratio is $latex q =M_2/M_1 \in [1,4]$. We discuss the construction of low-eccentricity puncture initial data for these cases, the properties of the final merged BH, and compare the last 8-10 GW cycles up to $latex M\omega = 0.1$ with the phase and amplitude predicted by standard post-Newtonian (PN) approximants. As in previous studies, we find that the phase from the 3.5PN TaylorT4 approximant is most accurate for nonspinning binaries. For equal-mass spinning binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN order) gives the most robust performance, but it is possible to treat TaylorT4 in such a way that it gives the best accuracy for spins $latex \chi_i > -0.75$. When high-order amplitude corrections are included, the PN amplitude of the $latex (\ell=2,m=\pm2)$ modes is larger than the NR amplitude by between 2-4%.

by Galley, Chad R. and Herrmann, Frank and Silberholz, John and Tiglio, Manuel and Guerberoff, Gustavo

We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal component analysis of spin and orbital angular momentum variables we systematically look for uncorrelated quantities and find three of them which are highly conserved in a statistical sense, both as functions of time and with respect to variations in initial spin orientations. We also look for and find the variables that account for the largest variations in the problem. We present binary black hole simulations of the full Einstein equations analyzing to what extent these results might carry over to the full theory in the inspiral and merger regimes. Among other applications these results should be useful both in semi-analytical and numerical building of templates of gravitational waves for gravitational wave detectors.

by Kesden, Michael and Sperhake, Ulrich and Berti, Emanuele
7 pages, 4 figures, submitted to ApJL

Numerical-relativity simulations indicate that the black hole produced in a binary merger can recoil with a velocity up to v_max ~ 4,000 km/s with respect to the center of mass of the initial binary. This challenges the paradigm that most galaxies form through hierarchical mergers, yet retain supermassive black holes at their centers despite having escape velocities much less than v_max. Interaction with a circumbinary disk can align the binary black hole spins with their orbital angular momentum, reducing the recoil velocity of the final black hole produced in the subsequent merger. However, the effectiveness of this alignment depends on highly uncertain accretion flows near the binary black holes. In this Letter, we show that if the spin S_1 of the more massive binary black hole is even partially aligned with the orbital angular momentum L, relativistic spin precession on sub-parsec scales can align the binary black hole spins with each other. This alignment significantly reduces the recoil velocity even in the absence of gas. For example, if the angle between S_1 and L at large separations is 10 degrees while the second spin S_2 is isotropically distributed, the spin alignment discussed in this paper reduces the median recoil from 864 km/s to 273 km/s for maximally spinning black holes with a mass ratio of 9/11. This reduction will greatly increase the fraction of galaxies retaining their supermassive black holes.

by Lubich, Christian and Walther, Benny and Bruegmann, Bernd
9 pages, 6 figures

We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In the context of the splitting, it is possible to integrate the individual terms of the spin-orbit and spin-spin Hamiltonians analytically, exploiting the special structure of the underlying equations of motion. The outcome is a symplectic, time-reversible integrator, which can be raised to arbitrary order by composition. A fourth-order version is shown to give excellent behavior concerning error growth and conservation of energy and angular momentum in long-term simulations. Favorable properties of the integrator are retained in the presence of weak dissipative forces due to radiation damping in the full post-Newtonian equations.

by Mueller, Doreen and Grigsby, Jason and Bruegmann, Bernd
10 pages, 14 figures

Certain numerical frameworks used for the evolution of binary black holes make use of a gamma driver, which includes a damping factor. Such simulations typically use a constant value for damping. However, it has been found that very specific values of the damping factor are needed for the calculation of unequal mass binaries. We examine carefully the role this damping plays, and provide two explicit, non-constant forms for the damping to be used with mass-ratios further from one. Our analysis of the resultant waveforms compares well against the constant damping case.

by van Meter, James R. and Miller, M. Coleman and Baker, John G. and Boggs, William D. and Kelly, Bernard J.
14 pages.

Although the gravitational wave kick velocity in the orbital plane of coalescing black holes has been understood for some time, apparently conflicting formulae have been proposed for the dominant out-of-plane kick, each a good fit to different data sets. This is important to resolve because it is only the out-of-plane kicks that can reach more than 500 km/s and can thus eject merged remnants from galaxies. Using a different ansatz for the out-of-plane kick, we show that we can fit almost all existing data to better than 5 %. This is good enough for any astrophysical calculation, and shows that the previous apparent conflict was only because the two data sets explored different aspects of the kick parameter space.

by Rezzolla, Luciano and Macedo, Rodrigo P. and Jaramillo, José Luis
4 pages

The generation of a large recoil velocity from the inspiral and merger of binary black holes represents one of the most exciting results of numerical-relativity calculations. While many aspects of this process have been investigated and explained, the “anti-kick”, namely the sudden deceleration after the merger, has not yet found a simple explanation. We show that the anti-kick can be easily understood in terms of the radiation from a deformed black hole where the intrinsically anisotropic curvature distribution on the horizon determines the direction and intensity of the recoil. Our analysis is focussed on the properties of Robinson-Trautman spacetimes and allows us to measure both the energies and momenta radiated in a gauge-invariant manner. At the same time, this simpler setup provides all the qualitative but also quantitative features of inspiralling black hole binaries, thus opening the way to a deeper understanding of the nonlinear dynamics of black-hole spacetimes.

by Berti, Emanuele and Cardoso, Vitor and Hinderer, Tanja and Lemos, Madalena and Pretorius, Frans and Sperhake, Ulrich and Yunes, Nicolas
29 pages, 19 figure, 6 tables

Ultrarelativistic collisions of black holes are ideal gedanken experiments to study the nonlinearities of general relativity. In this paper we use semianalytical tools to better understand the nature of these collisions and the emitted gravitational radiation. We explain many features of the energy spectra extracted from numerical relativity simulations using two complementary semianalytical calculations. In the first calculation we estimate the radiation by a “zero-frequency limit” analysis of the collision of two point particles with finite impact parameter. In the second calculation we replace one of the black holes by a point particle plunging with arbitrary energy and impact parameter into a Schwarzschild black hole, and we explore the multipolar structure of the radiation paying particular attention to the near-critical regime. We also use a geodesic analogy to provide qualitative estimates of the dependence of the scattering threshold on the black hole spin and on the dimensionality of the spacetime.

by Zanotti, Olindo and Rezzolla, Luciano and Del Zanna, Luca and Palenzuela, Carlos
17 pages, 11 figures, submitted to MNRAS, movies available at http://numrel.aei.mpg.de/Visualisations/Archive/BinaryBlackHoles/EMCounterparts/EMCounterparts.html

We investigate the dynamics of a circumbinary disc that responds to the loss of mass and to the recoil velocity of the black hole produced by the merger of a binary system of supermassive black holes. More specifically, we perform the first two-dimensional general relativistic hydrodynamics simulations of \textit{extended} non-Keplerian discs and employ a new technique to construct a “shock detector”, thus determining the precise location of the shocks produced in the accreting disc by the recoiling black hole. In this way we can study how the properties of the system, such as the spin, mass and recoil velocity of the black hole, affect the mass accretion rate and are imprinted on the electromagnetic emission from these sources. In contrast with what done in similar works, we here question the estimates of the bremsstrahlung luminosity when computed without properly taking into account the radiation transfer, thus yielding cooling times that are unrealistically short. At the same time we show, through an approximation based on the relativistic analogue of the isothermal evolution of \citet{Corrales2009}, that the luminosity produced can reach a peak value above $latex L \simeq 10^{43} {\rm erg/s} $ at about $latex \sim 20 {\rm d}$ after the merger of a binary with total mass $latex M\simeq 10^6 M_\odot$ and persist for several days at values which are a factor of a few smaller. If confirmed by more sophisticated calculations such a signal could indeed lead to an electromagnetic counterpart of the merger of binary black-hole system.

by Kesden, Michael and Sperhake, Ulrich and Berti, Emanuele
20 pages, 16 figures, revtex

The inspiral of binary black holes is governed by gravitational radiation reaction at binary separations r 10 M. Fortunately, binary evolution between these separations is well described by post-Newtonian equations of motion. We examine how this post-Newtonian evolution affects the distribution of spin orientations at separations r near 10 M where numerical-relativity simulations typically begin. Although isotropic spin distributions at r =1000 M remain isotropic at r = 10 M, distributions that are initially partially aligned with the orbital angular momentum can be significantly distorted during the post-Newtonian inspiral. Spin-orbit resonances tend to align (anti-align) the binary black hole spins with each other if the spins were initially partially aligned (anti-aligned) with respect to the orbital angular momentum, thus increasing (decreasing) the average final spin. Resonant effects are stronger for comparable-mass binaries, and they could produce significant spin alignment in massive black hole mergers at high redshifts and in stellar-mass black hole binaries. We also point out that precession induces an intrinsic accuracy limitation of 0.03 in the dimensionless spin magnitude, and about 20 degrees in the direction in predicting the final spin resulting from widely separated binary configurations.

by Hinder, Ian
14 pages; submitted to the Classical and Quantum Gravity special issue for NRDA2009

Since the breakthroughs in 2005 which have led to long term stable solutions of the binary black hole problem in numerical relativity, much progress has been made. I present here a short summary of the state of the field, including the capabilities of numerical relativity codes, recent physical results obtained from simulations, and improvements to the methods used to evolve and analyse binary black hole spacetimes.

by Campanelli, Manuela and Lousto, Carlos O. and Mundim, Bruno C. and Nakano, Hiroyuki and Zlochower, Yosef and Bischof, Hans-Peter
12 pages, 5 figures, Prepared for 8th Edoardo Amaldi Conference on Gravitational Waves (Amaldi8)

We review some of the recent dramatic developments in the fully nonlinear simulation of generic, highly-precessing, black-hole binaries, and introduce a new approach for generating hybrid post-Newtonian / Numerical waveforms for these challenging systems.

by Field, Scott E. and Hesthaven, Jan S. and Lau, Stephen R.
Uses revtex4, 23 pages, 9 figures, 3 tables

In the context of metric perturbation theory for non-spinning black holes, extreme mass ratio binary (EMRB) systems are described by distributionally forced master wave equations. Numerical solution of a master wave equation as an initial boundary value problem requires initial data. However, because the correct initial data for generic-orbit systems is unknown, specification of trivial initial data is a common choice, despite being inconsistent and resulting in a solution which is initially discontinuous in time. As is well known, this choice leads to a “burst” of junk radiation which eventually propagates off the computational domain. We observe another unintended consequence of trivial initial data: development of a persistent spurious solution, here referred to as the Jost junk solution, which contaminates the physical solution for long times. This work studies the influence of both types of junk on metric perturbations, waveforms, and self-force measurements, and it demonstrates that smooth modified source terms mollify the Jost solution and reduce junk radiation.

by Lousto, Carlos O. and Nakano, Hiroyuki and Zlochower, Yosef and Campanelli, Manuela
4 pages, 5 figures, revtex4

We study black-hole binaries in the intermediate-mass-ratio regime 0.01 < q < 0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO/VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully-nonlinear numerical simulations.

by Barausse, Enrico and Buonanno, Alessandra
22 pages, 9 figures

Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle’s spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass m, but also with a spin S*. Thus, the effective particle interacts with the effective Kerr background (having spin S_Kerr) through a geodesic-type interaction and an additional spin-dependent interaction proportional to S*. When expanded in post-Newtonian (PN) orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it reproduces all spin-orbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations.

by Mueller, Doreen and Bruegmann, Bernd
15 pages, submitted to CQG for NRDA 2009 conference proceedings

Moving puncture simulations of black hole binaries rely on a specific gauge choice that leads to approximately stationary coordinates near each black hole. Part of the shift condition is a damping parameter, which has to be properly chosen for stable evolutions. However, a constant damping parameter does not account for the difference in mass in unequal mass binaries. We introduce a position dependent shift damping that addresses this problem. Although the coordinates change, the changes in the extracted gravitational waves are small.

by Yunes, Nicolas and Pretorius, Frans and Spergel, David
11 pages, 2 figures, submitted to Phys. Rev. D

Space-borne gravitational wave detectors, such as the proposed Laser Interferometer Space Antenna, are expected to observe black hole coalescences to high redshift and with large signal-to-noise ratios, rendering their gravitational waves ideal probes of fundamental physics. The promotion of Newton’s constant to a time-function introduces modifications to the binary’s binding energy and the gravitational wave luminosity, leading to corrections in the chirping frequency. Such corrections propagate into the response function and, given a gravitational wave observation, they allow for constraints on the first time-derivative of Newton’s constant at the time of merger. We find that space-borne detectors could indeed place interesting constraints on this quantity as a function of sky position and redshift, providing a {\emph{constraint map}} over the entire range of redshifts where binary black hole mergers are expected to occur. A LISA observation of an equal-mass inspiral event with total redshifted mass of 10^5 solar masses for three years should be able to measure $latex \dot{G}/G$ at the time of merger to better than 10^(-11)/yr.

by Gold, Roman and Bruegmann, Bernd
8 pages, 5 figures, Amaldi8 conference proceedings

We study zoom-whirl behaviour of equal mass, non-spinning black hole binaries in full general relativity. The magnitude of the linear momentum of the initial data is fixed to that of a quasi-circular orbit, and its direction is varied. We find a global maximum in radiated energy for a configuration which completes roughly one orbit. The radiated energy in this case exceeds the value of a quasi-circular binary with the same momentum by 15%. The direction parameter only requires minor tuning for the localisation of the maximum. There is non-trivial dependence of the energy radiated on eccentricity (several local maxima and minima). Correlations with orbital dynamics shortly before merger are discussed. While being strongly gauge-dependent, these findings are intuitive from a physical point of view and support basic ideas about the efficiency of gravitational radiation from a binary system.

by Palenzuela, Carlos and Lehner, Luis and Yoshida, Shin
12 pages

In addition to producing loud gravitational waves (GW), the dynamics of a binary black hole system could induce emission of electromagnetic (EM) radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We here study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary’s dynamics induce a variability in possible electromagnetically induced emissions as well as an enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves.

by Zenginoglu, Anil
9 pages, 8 figures

We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge-Wheeler-Zerilli equations in time domain using hyperboloidal surfaces and a compactifying radial coordinate. We stress the importance of including the asymptotic region in the computational domain in studies of gravitational radiation. The hyperboloidal approach should be helpful in a wide range of applications employing black hole perturbation theory.

by Bode, Tanja and Haas, Roland and Bogdanovic, Tamara and Laguna, Pablo and Shoemaker, Deirdre
19 pages, 14 figures

Coincident detections of electromagnetic (EM) and gravitational wave (GW) signatures from coalescence events of supermassive black holes are the next observational grand challenge. Such detections will provide the means to study cosmological evolution and accretion processes associated with these gargantuan compact objects. More generally, the observations will enable testing general relativity in the strong, nonlinear regime and will provide independent cosmological measurements to high precision. Understanding the conditions under which coincidences of EM and GW signatures arise during supermassive black hole mergers is therefore of paramount importance. As an essential step towards this goal, we present results from the first fully general relativistic, hydrodynamical study of the late inspiral and merger of equal-mass, spinning supermassive black hole binaries in a gas cloud. We find that variable EM signatures correlated with GWs can arise in merging systems as a consequence of shocks and accretion combined with the effect of relativistic beaming. The most striking EM variability is observed for systems where spins are aligned with the orbital axis and where orbiting black holes form a stable set of density wakes, but all systems exhibit some characteristic signatures that can be utilized in searches for EM counterparts. In the case of the most massive binaries observable by the Laser Interferometer Space Antenna, calculated luminosities imply that they may be identified by EM searches to z = 1, while lower mass systems and binaries immersed in low density ambient gas can only be detected in the local universe.

by Farris, Brian D. and Liu, Yuk Tung and Shapiro, Stuart L.
33 pages, 24 Figures, two tables. Submitted to PRD

Merging supermassive black hole-black hole (BHBH) binaries produced in galaxy mergers are promising sources of detectable gravitational waves. If such a merger takes place in a gaseous environment, there is a possibility of a simultaneous detection of electromagnetic and gravitational radiation, as the stirring, shock heating and accretion of the gas may produce variability and enhancements in the electromagnetic flux. Such a simultaneous detection can provide a wealth of opportunities to study gravitational physics, accretion physics, and cosmology. We investigate this scenario by performing fully general relativistic, hydrodynamic simulations of merging, equal-mass, nonspinning BHBH binaries embedded in gas clouds. We evolve the metric using the BSSN formulation with standard moving puncture gauge conditions and handle the hydrodynamics via a high-resolution shock-capturing (HRSC) scheme. We consider both “binary Bondi accretion” in which the binary is at rest relative to the ambient gas cloud, as well as “binary Bondi-Hoyle-Lyttleton accretion” in which the binary moves relative to the gas cloud. The gas cloud is assumed to be homogeneous far from the binary and governed by a \Gamma-law equation of state. We vary \Gamma between 4/3 and 5/3. For each simulation, we compute the gas flow and accretion rate and estimate the electromagnetic luminosity due to bremsstrahlung and synchrotron emission. We find evidence for significant enhancements in both the accretion rate and luminosity over values for a single black hole of the same mass as the binary. We estimate that this luminosity enhancement should be detectable by LSST for a 10^6 M_sun binary in a hot gas cloud of density n~10/cm^3 and temperature T~10^6 K at z=1, reaching a maximum of L~3×10^43 erg/s, with the emission peaking in the visible band.

by Pollney, Denis and Reisswig, Christian and Schnetter, Erik and Dorband, Nils and Diener, Peter

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 $latex r\to\infty$ throughout the simulation, including the merger and ringdown. Ringdown frequencies for these modes (to $latex (\ell,m)=(6,6)$) match perturbative calculations to within 0.01%, providing a strong confirmation that the remnant settles to a Kerr black hole with irreducible mass $latex M_{\rm irr} = 0.884355\pm20\times10^{-6}$ and spin $latex S_f/M_f^2 = 0.686923 \pm 10\times10^{-6}$

by Khanna, Gaurav and McKennon, Justin
8 pages, 4 figures, Accepted for publication in Parallel and Distributed Computing and Systems (PDCS 2009)

In this paper, we accelerate a gravitational physics numerical modelling application using hardware accelerators — Cell processor and Tesla CUDA GPU. We describe these new technologies and our approach in detail, and then present our final performance results. We obtain well over an order-of-magnitude performance gain in our application by making use of these many-core architectures.

by Ajith, P. and Hannam, M. and Husa, S. and Chen, Y. and Bruegmann, B. and Dorband, N. and Mueller, D. and Ohme, F. and Pollney, D. and Reisswig, C. and Santamaria, L. and Seiler, J.
4 pages, 5 figures

We present the first analytical inspiral-merger-ringdown gravitational waveforms from black-hole (BH) binaries with non-precessing spins. By matching a post-Newtonian description of the inspiral to a set of numerical calculations performed in full general relativity, we obtain a waveform family with a conveniently small number of physical parameters. The physical content of these waveforms includes the “orbital hang-up” effect, when BHs are spinning rapidly along the direction of the orbital angular momentum. These waveforms will allow us to detect a larger parameter space of BH binary coalescence, to explore various scientific questions related to GW astronomy, and could dramatically improve the expected detection rates of GW detectors.

by Chu, Tony and Pfeiffer, Harald P. and Scheel, Mark A.
14 pages, 15 figures

High-accuracy binary black hole simulations are presented for black holes with spins anti-aligned with the orbital angular momentum. The particular case studied represents an equal-mass binary with spins of equal magnitude S/m^2=0.43757 \pm 0.00001. The system has initial orbital eccentricity ~4e-5, and is evolved through 10.6 orbits plus merger and ringdown. The remnant mass and spin are M_f=(0.961109 \pm 0.000003)M and S_f/M_f^2=0.54781 \pm 0.00001, respectively, where M is the mass during early inspiral. The gravitational waveforms have accumulated numerical phase errors of <~ 0.1 radians without any time or phase shifts, and <~ 0.01 radians when the waveforms are aligned with suitable time and phase shifts. The waveform is extrapolated to infinity using a procedure accurate to <~ 0.01 radians in phase, and the extrapolated waveform differs by up to 0.13 radians in phase and about one percent in amplitude from the waveform extracted at finite radius r=350M. The simulations employ different choices for the constraint damping parameters in the wave zone; this greatly reduces the effects of junk radiation, allowing the extraction of a clean gravitational wave signal even very early in the simulation.

by Herrmann, Frank and Silberholz, John and Bellone, Matias and Guerberoff, Gustavo and Tiglio, Manuel
Added one reference

We report on early results of a numerical and statistical study of binary black hole inspirals. The two black holes are evolved using post-Newtonian approximations starting with initially randomly distributed spin vectors. We characterize certain aspects of the distribution shortly before merger. In particular we note the uniform distribution of black hole spin vector dot products shortly before merger and a high correlation between the initial and final black hole spin vector dot products in the equal-mass, maximally spinning case. These simulations were performed on Graphics Processing Units, and we demonstrate a speed-up of a factor 50 over a more conventional CPU implementation.

by Vega, Ian and Diener, Peter and Tichy, Wolfgang and Detweiler, Steven
23 pages, 13 figures

Prescriptions for numerical self-force calculations have traditionally been designed for frequency-domain or (1+1) time-domain codes which employ a mode decomposition to facilitate in carrying out a delicate regularization scheme. This has prevented self-force analyses from benefiting from the powerful suite of tools developed and used by numerical relativists for simulations of the evolution of comparable-mass black hole binaries. In this work, we revisit a previously-introduced (3+1) method for self-force calculations, and demonstrate its viability by applying it to the test case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Two (3+1) codes originally developed for numerical relativity applications were independently employed, and in each we were able to compute the two independent components of the self-force and the energy flux correctly to within $latex < 1%$. We also demonstrate consistency between $latex t$-component of the self-force and the scalar energy flux. Our results constitute the first successful calculation of a self-force in a (3+1) framework, and thus open opportunities for the numerical relativity community in self-force analyses and the perturbative modeling of extreme-mass-ratio inspirals.

by Hannam, Mark and Husa, Sascha and Murchadha, Niall Ó
15 pages, 14 figures

The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum via the Bowen-York extrinsic curvature. When these data are evolved, they quickly approach a “trumpet” topology, suggesting that it would be preferable to use data that are in trumpet form from the outset. To achieve this, we extend the puncture method to allow the construction of Bowen-York trumpets, including an existence and uniqueness proof of the solutions. We construct boosted, spinning and binary Bowen-York puncture trumpets using a single-domain pseudospectral elliptic solver, and evolve the binary data and compare with standard wormhole-data results. We also show that the black-hole mass can be prescribed a priori, without recourse to the iterative procedure that is necessary for wormhole data.

by van Meter, James R. and Wise, John H. and Miller, M. Coleman and Reynolds, Christopher S. and Centrella, Joan M. and Baker, John G. and Boggs, William D. and Kelly, Bernard J. and McWilliams, Sean T.
5 pages, 4 figures

Coalescing massive black hole binaries are produced by the mergers of galaxies. The final stages of the black hole coalescence produce strong gravitational radiation that can be detected by the space-borne LISA. In cases where the black hole merger takes place in the presence of gas and magnetic fields, various types of electromagnetic signals may also be produced. Modeling such electromagnetic counterparts of the final merger requires evolving the behavior of both gas and fields in the strong-field regions around the black holes. We have taken a step towards solving this problem by mapping the flow of pressureless matter in the dynamic, 3-D general relativistic spacetime around the merging black holes. We find qualitative differences in collision and outflow speeds, including a signature of the merger when the net angular momentum of the matter is low, between the results from single and binary black holes, and between nonrotating and rotating holes in binaries. If future magnetohydrodynamic results confirm these differences, it may allow assessment of the properties of the binaries as well as yielding an identifiable electromagnetic counterpart to the attendant gravitational wave signal.

by Reisswig, C. and Bishop, N. T. and Pollney, D. and Szilagyi, B.
4 pages, 3 figures

The accurate calculation of gravitational radiation emitted during black hole merger events is important for both improving the chances of detecting such events, as well as for making an astrophysical interpretation of the data once an event has been detected. Gravitational radiation is properly defined only at future null infinity (denoted by Scri), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at Scri for the real astrophysical problem of the inspiral and merger of two equal mass non-spinning black holes (this problem has become a standard benchmark case in numerical relativity). Thus we have determined the first unambiguous merger waveforms for this problem. The implementation that has been developed is general purpose, and can be applied to calculate the gravitational radiation, at Scri, given data at a finite radius calculated in another computation.

by Sperhake, U. and Cardoso, V. and Pretorius, F. and Berti, E. and Hinderer, T. and Yunes, N.
4 pages, 4 pages, revtex

We study the collision of two highly boosted equal mass, nonrotating black holes with generic impact parameter. We find such systems to exhibit zoom-whirl behavior when fine tuning the impact parameter. Near the threshold of immediate merger, these systems can produce black holes rotating close to the Kerr limit and generate radiated energies as large as ~35% of the center of mass energy.

by Healy, James and Levin, Janna and Shoemaker, Deirdre

Zoom-whirl behavior has the reputation of being a rare phenomenon in comparable mass binaries. The concern has been that gravitational radiation would drain angular momentum so rapidly that generic orbits would circularize before zoom-whirl behavior could play out, and only rare highly tuned orbits would retain their imprint. Using full numerical relativity, we catch zoom-whirl behavior despite dissipation for a range of orbits. The larger the mass ratio, the longer the pair can spend in orbit before merging and therefore the more zooms and whirls that can be seen. Larger spins also enhance zoom-whirliness. An important implication is that these eccentric orbits can merge during a whirl phase, before enough angular momentum has been lost to truly circularize the orbit. In other words, although the whirl phase is nearly circular, merger of eccentric orbits occurs through a separatrix other than the isco. Gravitational waveforms from eccentric binaries will be modulated by the harmonics of zoom-whirl orbits, showing quiet phases during a zoom and louder glitches during whirls.

by Owen, Robert
12 pages, 13 figures

Methods are presented to define and compute source multipoles of dynamical horizons in numerical relativity codes, extending previous work from the isolated and dynamical horizon formalisms in a manner that allows for the consideration of horizons that are not axisymmetric. These methods are then applied to a binary black hole merger simulation, providing evidence that the final remnant is a Kerr black hole, both through the (spatially) gauge-invariant recovery of the geometry of the apparent horizon, and through a detailed extraction of quasinormal ringing modes directly from the strong-field region.

by Berti, Emanuele and Cardoso, Vitor and Starinets, Andrei O.
112 pages, 20 figures, 4 tables. Invited Topical Review for CQG. Comments and suggestions are welcome. QNM data and Mathematica notebooks are available at http://www.phy.olemiss.edu/~berti/qnms.html and http://gamow.ist.utl.pt/~vitor/ringdown

Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra requires solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.

by Palenzuela, Carlos and Anderson, Matthew and Lehner, Luis and Liebling, Steven L. and Neilsen, David
4 pages, 4 figures

In addition to producing gravitational waves (GW), the dynamics of a binary black hole system could induce emission of electromagnetic (EM) radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We here study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary’s dynamics induce a variability in possible electromagnetically induced emissions as well as a possible enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves.

by Laguna, Pablo and Larson, Shane L. and Spergel, David and Yunes, Nicolas
4 pages, 1 figure

Gravitational waves are messengers carrying valuable information about their sources. For sources at cosmological distances, the waves will contain also the imprint left by the intervening matter. The situation is in close analogy with cosmic microwave photons, for which the large-scale structures the photons traverse contribute to the observed temperature anisotropies, in a process known as the integrated Sachs-Wolfe effect. We derive the gravitational wave counterpart of this effect for waves propagating on a Friedman-Robertson-Walker background with scalar perturbations. We find that the phase, frequency and amplitude of the gravitational waves experience Sachs-Wolfe type integrated effects, this in addition to the magnification effects on the amplitude from gravitational lensing. We show that for supermassive black hole binaries, the integrated effects could account for measurable changes on the frequency, chirp mass and luminosity distance of the binary, thus unveiling the presence of inhomogeneities, and potentially dark energy, in the Universe.

by Barausse, Enrico and Rezzolla, Luciano
4 pages, 2 figures

The knowledge of the spin of the black hole resulting from the merger of a generic binary system of black holes is of great importance to study the cosmological evolution of supermassive black holes. Several attempts have been recently made to model the spin via simple expressions exploiting the results of numerical-relativity simulations. While these expressions are in good agreement with the simulations, they are intrinsically imprecise when predicting the final spin direction, especially if applied to binaries with separations of hundred or thousands of gravitational radii. This is due to neglecting the precession of the orbital plane of the binary, and is a clear drawback if the formulas are employed in cosmological merger-trees or N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of thousands of gravitational radii. We remove this problem by proposing an expression which is built on improved assumptions and that gives, for any separation, a very accurate prediction both for the norm of the final spin and for its direction. By comparing with the numerical data, we also show that the final spin direction is very accurately aligned with the total angular momentum of the binary at large separation. Hence, observations of the final spin direction (e.g. via a jet) can provide information on the orbital plane of the binary at large separations and could be relevant, for instance, to study X-shaped radio sources.

by Canizares, Priscilla and Sopuerta, Carlos F.
15 pages, 9 figures, Revtex 4. Minor changes to match published version

The description of the inspiral of a stellar-mass compact object into a massive black hole sitting at a galactic centre is a problem of major relevance for the future space-based gravitational-wave observatory LISA (Laser Interferometer Space Antenna), as the signals from these systems will be buried in the data stream and accurate gravitational-wave templates will be needed to extract them. The main difficulty in describing these systems lies in the estimation of the gravitational effects of the stellar-mass compact object on his own trajectory around the massive black hole, which can be modeled as the action of a local force, the self-force. In this paper, we present a new time-domain numerical method for the computation of the self-force in a simplified model consisting of a charged scalar particle orbiting a nonrotating black hole. We use a multi-domain framework in such a way that the particle is located at the interface between two domains so that the presence of the particle and its physical effects appear only through appropriate boundary conditions. In this way we eliminate completely the presence of a small length scale associated with the need of resolving the particle. This technique also avoids the problems associated with the impact of a low differentiability of the solution in the accuracy of the numerical computations. The spatial discretization of the field equations is done by using the pseudospectral collocation method and the time evolution, based on the method of lines, uses a Runge-Kutta solver. We show how this special framework can provide very efficient and accurate computations in the time domain, which makes the technique amenable for the intensive computations required in the astrophysically-relevant scenarios for LISA.

by Santamaria, Lucia and Krishnan, Badri and Whelan, John T.
13 pages, 4 figures, to appear in the proceedings of the NRDA08 meeting, Syracuse, Aug. 11-14, 2008

Recent progress in numerical relativity now allows computation of the binary black hole merger, whereas post-Newtonian and perturbative techniques can be used to model the inspiral and ringdown phases. So far, most gravitational-wave searches have made use of various post-Newtonian-inspired templates to search for signals arising from the coalescence of compact binary objects. Ajith et al have produced hybrid waveforms for non-spinning binary black-hole systems which include the three stages of the coalescence process, and constructed from them phenomenological templates which capture the features of these waveforms in a parametrized form. As a first step towards extending the present inspiral searches to higher-mass binary black-hole systems, we have used these phenomenological waveforms in a search for numerically-simulated signals injected into synthetic LIGO data as part of the NINJA project.

by Aylott, Benjamin and Baker, John G. and Boggs, William D. and Boyle, Michael and Brady, Patrick R. and Brown, Duncan A. and Brügmann, Bernd and Buchman, Luisa T. and Buonanno, Alessandra and Cadonati, Laura and Camp, Jordan and Campanelli, Manuela and Centrella, Joan and Chatterji, Shourov and Christensen, Nelson and Chu, Tony and Diener, Peter and Dorband, Nils and Etienne, Zachariah B. and Faber, Joshua and Fairhurst, Stephen and Farr, Benjamin and Fischetti, Sebastian and Guidi, Gianluca and Goggin, Lisa M. and Hannam, Mark and Herrmann, Frank and Hinder, Ian and Husa, Sascha and Kalogera, Vicky and Keppel, Drew and Kidder, Lawrence E. and Kelly, Bernard J. and Krishnan, Badri and Laguna, Pablo and Lousto, Carlos O. and Mandel, Ilya and Marronetti, Pedro and Matzner, Richard and McWilliams, Sean T. and Matthews, Keith D. and Mercer, R. Adam and Mohapatra, Satyanarayan R. P. and Mroué, Abdul H. and Nakano, Hiroyuki and Ochsner, Evan and Pan, Yi and Pekowsky, Larne and Pfeiffer, Harald P. and Pollney, Denis and Pretorius, Frans and Raymond, Vivien and Reisswig, Christian and Rezzolla, Luciano and Rinne, Oliver and Robinson, Craig and Röver, Christian and Santamaría, Lucía and Sathyaprakash, Bangalore and Scheel, Mark A. and Schnetter, Erik and Seiler, Jennifer and Shapiro, Stuart L. and Shoemaker, Deirdre and Sperhake, Ulrich and Stroeer, Alexander and Sturani, Riccardo and Tichy, Wolfgang and Liu, Yuk Tung and van der Sluys, Marc and van Meter, James R. and Vaulin, Ruslan and Vecchio, Alberto and Veitch, John and Viceré, Andrea and Whelan, John T. and Zlochower, Yosef
53 pages, 25 figures

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.

by Hannam, Mark
22 pages, 6 figures, Version to be published in CQG, NRDA 2008 Special Issue

It is now possible to theoretically calculate the gravitational-wave signal from the inspiral, merger and ringdown of a black-hole-binary system. The late inspiral, merger and ringdown can be calculated in full general relativity using numerical methods. The numerical waveforms can then be either stitched to inspiral waveforms predicted by approximation techniques (in particular post-Newtonian calculations) that start at an arbitrarily low frequency, or used to calibrate free parameters in analytic models of the full waveforms. In this review I summarize the status of numerical-relativity (NR) waveforms that include at least ten cycles of the dominant mode of the GW signal before merger, which should be long enough to produce accurate, complete waveforms for GW observations.

by Walther, Benny and Bruegmann, Bernd and Mueller, Doreen
20 pages, 11 figures, pdflatex

Black hole binaries on non-eccentric orbits form an important subclass of gravitational wave sources, but it is a non-trivial issue to construct numerical initial data with minimal initial eccentricity for numerical simulations. We compute post-Newtonian orbital parameters for quasi-spherical orbits using the method of Buonanno, Chen and Damour (2006) and examine the resulting eccentricity in numerical simulations. Four different methods are studied resulting from the choice of Taylor-expanded or effective-one-body Hamiltonians, and from two choices for the energy flux. The eccentricity increases for unequal masses and for spinning black holes, but remains smaller than that obtained from previous post-Newtonian approaches. The effective-one-body Hamiltonian offers advantages for decreasing initial separation as expected, but in the context of this study also performs significantly better than the Taylor-expanded Hamiltonian for binaries with spin.