by Blanchet, Luc and Detweiler, Steven and Tiec, Alexandre Le and Whiting, Bernard F.
29 pages, 3 figures; to appear in the book “Mass and Motion in General Relativity”, proceedings of the C.N.R.S. School in Orleans, France, eds. L. Blanchet, A. Spallicci and B. F. Whiting

The relativistic motion of a compact binary system moving in circular orbit is investigated using the post-Newtonian (PN) approximation and the perturbative self-force (SF) formalism. A particular gauge-invariant observable quantity is computed as a function of the binary’s orbital frequency. The conservative effect induced by the gravitational SF is obtained numerically with high precision, and compared to the PN prediction developed to high order. The PN calculation involves the computation of the 3PN regularized metric at the location of the particle. Its divergent self-field is regularized by means of dimensional regularization. The poles proportional to 1/(d-3) which occur within dimensional regularization at the 3PN order disappear from the final gauge-invariant result. The leading 4PN and next-to-leading 5PN conservative logarithmic contributions originating from gravitational-wave tails are also obtained. Making use of these exact PN results, some previously unknown PN coefficients are measured up to the very high 7PN order by fitting to the numerical self-force data. Using just the 2PN and new logarithmic terms, the value of the 3PN coefficient is also confirmed numerically with very high precision. The consistency of this cross-cultural comparison provides a crucial test of the very different regularization methods used in both SF and PN formalisms, and illustrates the complementarity of these approximation schemes when modelling compact binary systems.

by Nichols, David A. and Chen, Yanbei
13 pages, 6 figures, 1 table, revtex4 format

Black-hole-binary coalescence is often divided into three stages: inspiral, merger and ringdown. The post-Newtonian (PN) approximation treats the inspiral phase, black-hole perturbation (BHP) theory describes the ringdown, and the nonlinear dynamics of spacetime characterize the merger. In this paper, we introduce a hybrid method that incorporates elements of PN and BHP theories, and we apply it to the head-on collision of black holes with transverse, anti-parallel spins. We compare our approximation technique with a full numerical-relativity simulation, and we find good agreement between the gravitational waveforms and the radiated energy and momentum. Our results suggest that PN and BHP theories may suffice to explain the main features of outgoing gravitational radiation for head-on mergers. This would further imply that linear perturbations to exact black-hole solutions can capture the nonlinear aspects of head-on binary-black-hole mergers accessible to observers far from the collision.

by Tessmer, Manuel and Schaefer, Gerhard
28 pages

The article provides ready-to-use 1pN-accurate frequency-domain gravitational wave forms for eccentric nonspinning compact binaries of arbitrary mass ratio including the first post-Newtonian (1pN) point particle corrections to the far-zone gravitational wave amplitude, given in terms of tensor spherical harmonics. The averaged equations for the decay of the eccentricity and growth of radial frequency due to radiation reaction are used to provide stationary phase approximations to the frequency-domain wave forms.

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 Gergely, László Á. and Biermann, Peter L. and Caramete, Laurenţiu I.
11 pages, 2 figures

During post-Newtonian evolution of a compact binary, a mass ratio different from one provides a second small parameter, which can lead to unexpected results. We present a statistics of supermassive black hole candidates, which enables us first to derive their mass distribution, then to establish a logarithmically even probability of the mass ratios at their encounter. In the mass ratio range (1/30,1/3) of supermassive black hole mergers representing 40% of all possible cases, the combined effect of spin-orbit precession and gravitational radiation leads to a spin-flip of the dominant spin during the inspiral phase of the merger. This provides a mechanism for explaining a large set of observations on X-shaped radio galaxies. In another 40%, with mass ratios (1/30,1/1000) a spin-flip never happens, while in the remaining 20% of mergers with mass ratios (1/3,1) it may occur during the plunge. We analyze the magnitude of the spin-flip angle occurring during the inspiral as function of the mass ratio and original relative orientation of the spin and orbital angular momentum. We also derive a formula for the final spin at the end of the inspiral in this mass ratio range.

by Klein, Antoine and Jetzer, Philippe
7 pages, 1 figure; Accepted for publication in Phys. Rev. D

We compute here the spin-orbit and spin-spin couplings needed for an accurate computation of the phasing of gravitational waves emitted by comparable-mass binaries on eccentric orbits at the second post-Newtonian (PN) order. We use a quasi-Keplerian parametrization of the orbit free of divergencies in the zero eccentricity limit. We find that spin-spin couplings induce a residual eccentricity for coalescing binaries at 2PN, of the order of $latex 10^{-4}$-$latex 10^{-3}$ for supermassive black hole binaries in the LISA band. Spin-orbit precession also induces a non-trivial pattern in the evolution of the eccentricity, which could help to reduce the errors on the determination of the eccentricity and spins in a gravitational wave measurement.

by Cornish, Neil J. and Key, Joey Shapiro
9 pages

Several scenarios have been proposed in which the orbits of binary black holes enter the band of a gravitational wave detector with significant eccentricity. To avoid missing these signals or biasing the parameter estimation it is important that we consider waveform models that account for eccentricity. The ingredients needed to compute post-Newtonian (PN) waveforms produced by spinning black holes inspiralling on quasi-eccentric orbits have been available for almost two decades at 2 PN order, and this work has recently been extended to 2.5 PN order. However, the computational cost of directly implementing these waveforms is high, requiring many steps per orbit to evolve the system of coupled differential equations. Here we employ a separation of timescales and a generalized Keplarian parameterization of the orbits to produce efficient waveforms describing spinning black hole binaries with arbitrary spin orientations on quasi-eccentric orbits to 1.5 PN order. Our solution includes the spin contributions to the decay of the semi-major axis and eccentricity. We outline a scheme for extending our approach to higher post-Newtonian order.

by Hergt, Steven and Steinhoff, Jan and Schaefer, Gerhard
11 pages, submitted to CQG

Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components like black holes and/or neutron stars taking into account spin-induced quadrupolar deformation effects in second post-Newtonian order perturbation theory of Einstein’s field equations. The corresponding equations of motion for spin, position and momentum variables are given in terms of canonical Poisson brackets. Comparison with a nonreduced potential calculated within the Effective Field Theory approach is made.

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 Favata, Marc
11 pages, 2 figures; proceedings of the 8th Amaldi Conference on Gravitational Waves (New York, June 2009); accepted for publication in special issue of Classical and Quantum Gravity

The nonlinear memory effect is a slowly-growing, non-oscillatory contribution to the gravitational-wave amplitude. It originates from gravitational waves that are sourced by the previously emitted waves. In an ideal gravitational-wave interferometer a gravitational-wave with memory causes a permanent displacement of the test masses that persists after the wave has passed. Surprisingly, the nonlinear memory affects the signal amplitude starting at leading (Newtonian-quadrupole) order. Despite this fact, the nonlinear memory is not easily extracted from current numerical relativity simulations. After reviewing the linear and nonlinear memory I summarize some recent work, including: (1) computations of the memory contribution to the inspiral waveform amplitude (thus completing the waveform to third post-Newtonian order); (2) the first calculations of the nonlinear memory that include all phases of binary black hole coalescence (inspiral, merger, ringdown); and (3) realistic estimates of the detectability of the memory with LISA.

by Tessmer, Manuel and Hartung, Johannes and Schaefer, Gerhard
26 pages, 1 figure

A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin orbit and 1PN spin-spin contributions, where the spins are counted of 0PN order.

by Rothe, Tilman J. and Schäfer, Gerhard
18 pages, no figures

The recently constructed Hamiltonians for spinless binary black holes through third post-Newtonian order and for spinning ones through formal second post-Newtonian order, where the spins are counted of zero post-Newtonian order, are transformed into fully canonical center-of-mass and rest-frame variables. The mixture terms in the Hamiltonians between center-of-mass and rest-frame variables are in accordance with the relation between the total linear momentum and the center-of-mass velocity as demanded by global Lorentz invariance. The various generating functions for the center-of-mass and rest-frame canonical variables are explicitly given in terms of the single-particle canonical variables. The no-interaction theorem does not apply because the world-line condition of Lorentz covariant position variables is not imposed.

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 Blanchet, Luc and Detweiler, Steven and Tiec, Alexandre Le and Whiting, Bernard F.
32 pages, 2 figures

We continue a previous work on the comparison between the post-Newtonian (PN) approximation and the gravitational self-force (SF) analysis of circular orbits in a Schwarzschild background. We show that the numerical SF data contain physical information corresponding to extremely high PN approximations. We find that knowing analytically determined appropriate PN parameters helps tremendously in allowing the numerical data to be used to obtain higher order PN coefficients. Using standard PN theory we compute analytically the leading 4PN and the next-to-leading 5PN logarithmic terms in the conservative part of the dynamics of a compact binary system. The numerical perturbative SF results support well the analytic PN calculations through first order in the mass ratio, and are used to accurately measure the 4PN and 5PN non-logarithmic coefficients in a particular gauge invariant observable. Furthermore we are able to give estimates of higher order contributions up to the 7PN level. In our best fit we also confirm with high precision the value of the 3PN coefficient. This interplay between PN and SF efforts is important for the synthesis of template waveforms of extreme mass ratio inspirals to be analysed by the space-based gravitational wave instrument LISA. Our work will also have an impact on efforts that combine numerical results in a quantitative analytical framework so as to generate complete inspiral waveforms for the ground-based detection of gravitational waves by instruments such as LIGO and Virgo.

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 Itoh, Yousuke
38 pages, no figures. Accepted for publication in Phys. Rev. D

We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric non-rotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show that the locally defined energy of the star has a simple relation with its mass up to the 3.5 PN order.

by Damour, Thibault and Nagar, Alessandro
21 pages, 5 figures. Submitted to Phys. Rev. D

The late part of the gravitational wave signal of binary neutron star inspirals can in principle yield crucial information on the nuclear equation of state via its dependence on relativistic tidal parameters. In the hope of analytically describing the gravitational wave phasing during the late inspiral (essentially up to contact) we propose an extension of the effective one body (EOB) formalism which includes tidal effects. We compare the prediction of this tidal-EOB formalism to recently computed nonconformally flat quasi-equilibrium circular sequences of binary neutron star systems. Our analysis suggests the importance of higher-order (post-Newtonian) corrections to tidal effects, even beyond the first post-Newtonian order, and their tendency to {\it significantly} increase the “effective tidal polarizability” of neutron stars. We compare the EOB predictions to some recently advocated, nonresummed, post-Newtonian based (“Taylor-T4”) description of the phasing of inspiralling systems. This comparison shows the strong sensitivity of the late-inspiral phasing to the choice of the analytical model, but raises the hope that a sufficiently accurate numerical–relativity–“calibrated” EOB model might give us a reliable handle on the nuclear equation of state

by Gergely, László Árpád
12 pages, 2 figures

We establish the set of independent variables suitable to monitor the complicated evolution of the spinning compact binary during the inspiral. Our approach is valid up to the second post-Newtonian order, including spin and mass quadrupolar effects, for generic (noncircular, nonspherical) orbits. Then we analyze the conservative spin dynamics in terms of these variables. We prove that the only precessing and spinning black hole or neutron star binary configuration which is preserved by the post-Newtonian evolution with spin-spin and quadrupole-monopole contributions included is the equal mass, equal and identically oriented spin configuration. This analytic result puts severe limitations on what particular configurations can be selected in numerical investigations of compact binary evolutions, even in those including only the last orbits of the inspiral.

by Barausse, Enrico
5 pages, 3 figures. Submitted as proceeding of the 8th Amaldi International Conference on Gravitational Waves, NYC, 21-26 June 2009

The prediction of the spin of the black hole resulting from the merger of a generic black-hole binary system 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. Here I compare the results of all the simulations appeared so far in the literature with various formulas for the final spin magnitude and direction. I show that although all the formulas give reasonable results for the final spin magnitude, only the formula that I recently proposed in (Barausse & Rezzolla, Apj 704 L40) accurately predicts the final spin direction when applied to binaries with separations of hundred or thousands of gravitational radii. This makes my formula particularly suitable for cosmological merger-trees and N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of thousands of gravitational radii, and happens because my formula takes into account the post-Newtonian precession of the spins in a consistent manner.

by Damour, Thibault
44 pages

We discuss various ways in which the computation of conservative Gravitational Self Force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the Effective One-Body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity (NR) data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass NR data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focussing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian expansions of various (EOB and GSF) functions at the fourth post-Newtonian (4PN) level, and we analytically compute the first logarithm entering a certain, gauge-invariant “redshift” GSF function (defined along the sequence of circular orbits).

by Tiec, Alexandre Le and Blanchet, Luc and Will, Clifford M.
9 pages, 5 figures

The gravitational recoil or “kick” of a black hole formed from the merger of two orbiting black holes, and caused by the anisotropic emission of gravitational radiation, is an astrophysically important phenomenon. We combine (i) an earlier calculation, using post-Newtonian theory, of the kick velocity accumulated up to the merger of two non-spinning black holes, (ii) a “close-limit approximation” calculation of the radiation emitted during the ringdown phase, and based on a solution of the Regge-Wheeler and Zerilli equations using initial data accurate to second post-Newtonian order. We prove that ringdown radiation produces a significant “anti-kick”. Adding the contributions due to inspiral, merger and ringdown phases, our results for the net kick velocity agree with those from numerical relativity to 10-15 percent over a wide range of mass ratios, with a maximum velocity of 180 km/s at a mass ratio of 0.38.

by Tiec, Alexandre Le and Blanchet, Luc
34 pages, 6 figures

The ringdown phase of a black hole formed from the merger of two orbiting black holes is described by means of the close-limit (CL) approximation starting from second-post-Newtonian (2PN) initial conditions. The 2PN metric of point-particle binaries is formally expanded in CL form and identified with that of a perturbed Schwarzschild black hole. The multipolar coefficients describing the even-parity (or polar) and odd-parity (axial) components of the linear perturbation consistently satisfy the 2PN-accurate perturbative field equations. We use these coefficients to build initial conditions for the Regge-Wheeler and Zerilli wave equations, which we then evolve numerically. The ringdown waveform is obtained in two cases: head-on collision with zero-angular momentum, composed only of even modes, and circular orbits, for which both even and odd modes contribute. In a separate work, this formalism is applied to the study of the gravitational recoil produced during the ringdown phase of coalescing binary black holes.

by Schaefer, Gerhard
44 pages, to appear in the book “Mass and Motion in General Relativity”, proceedings of the CNRS School in Orleans/France, eds. L. Blanchet, A. Spallicci, and B. Whiting

A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field equations, the generalized isotropic ones of the canonical formalism of Arnowitt, Deser, and Misner and the harmonic ones of the Lorentz-covariant Fock-de Donder approach. Conserved quantities of isolated systems are identified and the Poincar\’e algebra is introduced. Post-Newtonian expansions are performed in the near and far (radiation) zones. The natural fitting of multipole expansions to post-Newtonian schemes is emphasized. The treated matter models are ideal fluids, pure point masses, and point masses with spin and mass-quadrupole moments modelling rotating black holes. Various Hamiltonians of spinning binaries are presented in explicit forms to higher post-Newtonian orders. The delicate use of black holes in post-Newtonian expansion calculations and of the Dirac delta function in general relativity find discussions.

by Blanchet, Luc and Detweiler, Steven and Tiec, Alexandre Le and Whiting, Bernard F.
36 pages, 3 figures

The problem of a compact binary system whose components move on circular orbits is addressed using two different approximation techniques in general relativity. The post-Newtonian (PN) approximation involves an expansion in powers of v/c<<1, and is most appropriate for small orbital velocities v. The perturbative self-force (SF) analysis requires an extreme mass ratio m1/m2<<1 for the components of the binary. A particular coordinate-invariant observable is determined as a function of the orbital frequency of the system using these two different approximations. The post-Newtonian calculation is pushed up to the third post-Newtonian (3PN) order. It involves the metric generated by two point particles and evaluated at the location of one of the particles. We regularize the divergent self-field of the particle by means of dimensional regularization. We show that the poles proportional to 1/(d-3) appearing in dimensional regularization at the 3PN order cancel out from the final gauge invariant observable. The 3PN analytical result, through first order in the mass ratio, and the numerical SF calculation are found to agree well. The consistency of this cross cultural comparison confirms the soundness of both approximations in describing compact binary systems. In particular, it provides an independent test of the very different regularization procedures invoked in the two approximation schemes.

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 Gergely, László Á. and Biermann, Peter L. and Mikóczi, Balázs and Keresztes, Zoltán
10 pages, to appear in Class. Quantum Grav. GWDAW13 Proceedings Special Issue, v2: no typos conjecture

We analyze galactic black hole mergers and their emitted gravitational waves. Such mergers have typically unequal masses with mass ratio of the order 1/10. The emitted gravitational waves carry the inprint of spins and mass quadrupoles of the binary components. Among these contributions, we consider here the quasi-precessional evolution of the spins. A method of taking into account these third post-Newtonian (3PN) effects by renormalizing (redefining) the 1.5 PN and 2PN accurate spin contributions to the accumulated orbital phase is developed.

by Arun, K. G. and Blanchet, Luc and Iyer, Bala R. and Sinha, Siddhartha
62 pages, 23 figures, article submitted

The angular momentum flux from an inspiralling binary system of compact objects moving in quasi-elliptical orbits is computed at the third post-Newtonian (3PN) order using the multipolar post-Minkowskian wave generation formalism. The 3PN angular momentum flux involves the instantaneous, tail, and tail-of-tails contributions as for the 3PN energy flux, and in addition a contribution due to non-linear memory. We average the angular momentum flux over the binary’s orbit using the 3PN quasi-Keplerian representation of elliptical orbits. The averaged angular momentum flux provides the final input needed for gravitational wave phasing of binaries moving in quasi-elliptical orbits. We obtain the evolution of orbital elements under 3PN gravitational radiation reaction in the quasi-elliptic case. For small eccentricities, we give simpler limiting expressions relevant for phasing up to order $latex e^2$. This work is important for the construction of templates for quasi-eccentric binaries, and for the comparison of post-Newtonian results with the numerical relativity simulations of the plunge and merger of eccentric binaries.

by Barausse, E. and Racine, E. and Buonanno, A.
17 pages

Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test-particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase-space algebra in the Newton-Wigner spin supplementary condition (SSC), suitably generalized to curved spacetime, and find that the phase-space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner (ADM) canonical Hamiltonian computed in PN theory in the test-particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type S_Kerr S (and S_Kerr^2) through 3PN order, S_Kerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test-particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.

by Blanchet, Luc
42 pages, to appear in the book “Mass and Motion in General Relativity”, proceedings of the C.N.R.S. School in Orleans, France, eds. L. Blanchet, A. Spallicci and B. Whiting

Reliable predictions of general relativity theory are extracted using approximation methods. Among these, the powerful post-Newtonian approximation provides us with our best insights into the problems of motion and gravitational radiation of systems of compact objects. This approximation has reached an impressive mature status, because of important progress regarding its theoretical foundations, and the successful construction of templates of gravitational waves emitted by inspiralling compact binaries. The post-Newtonian predictions are routinely used for searching and analyzing the very weak signals of gravitational waves in current generations of detectors. High-accuracy comparisons with the results of numerical simulations for the merger and ring-down of binary black holes are going on. In this article we give an overview on the general formulation of the post-Newtonian approximation and present up-to-date results for the templates of compact binary inspiral.

by Johnson-McDaniel, Nathan K. and Yunes, Nicolas and Tichy, Wolfgang and Owen, Benjamin J.
48 pages, 23 figures

(Abridged) By asymptotically matching a post-Newtonian (PN) metric to two tidally perturbed Schwarzschild metrics, we generate approximate initial data (in the form of a 4-metric) for a nonspinning black hole binary in a circular orbit. We carry out this matching through O(v^4) in the binary’s orbital velocity v, so the resulting data are conformally curved. Far from the holes, we use the appropriate PN metric that accounts for retardation, which we construct using the highest-order PN expressions available to compute the binary’s past history. The data set’s uncontrolled remainders are thus O(v^5) throughout the timeslice; we also generate an extension to the data set that has uncontrolled remainders of O(v^6) in the purely PN portion of the timeslice (i.e., not too close to the holes). The resulting data are smooth, since we join all the metrics together by smoothly interpolating between them. We perform this interpolation using transition functions constructed to avoid introducing excessive additional constraint violations. Due to their inclusion of tidal deformations and outgoing radiation, these data should substantially reduce the initial spurious (”junk”) radiation observed in current simulations that use conformally flat initial data. Such reductions in the nonphysical components of the initial data will be necessary for simulations to achieve the accuracy required to supply Advanced LIGO and LISA with the templates necessary for parameter estimation.

by Buonanno, Alessandra and Iyer, Bala and Ochsner, Evan and Pan, Yi and Sathyaprakash, B. S.
27 pages, 8 figures, 4 tables, submitted to PRD

The two-body dynamics in general relativity has been solved perturbatively using the post-Newtonian (PN) approximation. The evolution of the orbital phase and the emitted gravitational radiation are now known to a rather high order up to O(v^8), v being the characteristic velocity of the binary. The orbital evolution, however, cannot be specified uniquely due to the inherent freedom in the choice of parameter used in the PN expansion as well as the method pursued in solving the relevant differential equations. The goal of this paper is to determine the (dis)agreement between different PN waveform families in the context of initial and advanced gravitational-wave detectors. The waveforms employed in our analysis are those that are currently used by Initial LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the Fourier-domain representation TaylorF2. We examine the overlaps of these models with one another and with the prototype effective one-body model (calibrated to numerical relativity simulations, as currently used by initial LIGO) for a number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their differences and to help us decide whether there exist preferred families that are the most appropriate as search templates. We conclude that as long as the total mass remains less than a certain upper limit M_crit, all template families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial, Enhanced and Advanced LIGO. From a purely computational point of view we recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to numerical relativity simulations be used for total binary mass M > Mcrit.

by Fujita, Ryuichi and Hikida, Wataru

We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $latex \lambda$ as the independent variable. Mino time decouples the radial and polar motion of a particle and hence leads to forms more useful to estimate three fundamental frequencies, radial, polar and azimuthal motion, for the bound timelike geodesics in Kerr spacetime. This paper gives the first derivation of the analytical expressions of the fundamental frequencies. This paper also gives the first derivation of the analytical expressions of all coordinates for the bound timelike geodesics using Mino time. These analytical expressions should be useful not only to investigate physical properties of Kerr geodesics but more importantly to applications related to the estimation of gravitational waves from the extreme mass ratio inspirals.

by Galley, Chad R. and Hu, Bei-Lok
17 pages, 3 figures, Invited contribution to the International Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields (IARD) held at the Aristotle University, Thessaloniki, Greece, 22-26 June 2008. Proceedings to appear in Foundations of Physics

We present a new analytical framework for describing the dynamics of a gravitational binary system with unequal masses moving with arbitrary relative velocity, taking into account the backreaction from both compact objects in the form of tidal deformation, gravitational waves and self forces. Allowing all dynamical variables to interact with each other in a self-consistent manner this formalism ensures that all the dynamical quantities involved are conserved on the background spacetime and obey the gauge invariance under general coordinate transformations that preserve the background geometry. Because it is based on a generalized perturbation theory and the important new emphasis is on the self-consistency of all the dynamical variables involved we call it a gravitational perturbation theory with self-consistent backreaction (GP-SCB).

As an illustration of how this formalism is implemented we construct perturbatively a self-consistent set of equations of motion for an inspiraling gravitational binary, which does not require extra assumptions such as slow motion, weak-field or small mass ratio for its formulation. This case should encompass the inspiral and possibly the plunge and merger phases of binaries with otherwise general parameters (e.g., mass ratio and relative velocity) though more investigation is needed to substantiate it.

In the second part, we discuss how the mass ratio can be treated as a perturbation parameter in the post-Newtonian effective field theory (PN-EFT) approach, thus extending the work of Goldberger and Rothstein for equal mass binaries to variable mass ratios. We provide rough estimates for the higher post-Newtonian orders needed to determine the number of gravitational wave cycles, with a specified precision, that fall into a detector’s bandwidth.

by Yunes, Nicolas and Arun, K. G. and Berti, Emanuele and Will, Clifford M.
24 pages, 9 figures, submitted to Phys. Rev. D

We lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waveforms produced by eccentric, inspiraling compact binaries in a post-circular or small-eccentricity approximation. The time-dependent, “plus” and “cross” polarizations are expanded in Bessel functions, which are then self-consistently re-expanded in a power series about zero initial eccentricity to eighth order. The stationary phase approximation is then employed to obtain explicit analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify this framework by considering Newtonian-accurate waveforms, which in the post-circular scheme give rise to higher harmonics of the orbital phase and amplitude corrections both to the amplitude and the phase of the Fourier domain waveform. Such higher harmonics lead to an effective increase in the inspiral mass reach of a detector as a function of the binary’s eccentricity $latex e_0$ at the time when the binary enters the detector sensitivity band. Using the largest initial eccentricity allowed by our approximations ($latex e_0 < 0.4$), the mass reach is found to be enhanced up to factors of approximately 5 relative to that of circular binaries for Advanced LIGO, LISA, and the proposed Einstein Telescope at a signal-to-noise ratio of ten. A post-Newtonian generalization of the post circular scheme is also discussed, which holds the promise to provide “ready-to-use” Fourier-domain waveforms for data analysis of eccentric inspirals.

by Arun, K G and Will, Clifford M
12 pages, 4 figures

Observations by laser interferometric detectors of gravitational waves from inspiraling compact binary systems can be used to search for a dependence of the waves’ propagation speed on wavelength, and thereby to bound the mass or Compton wavelength of a putative graviton. We study the effect of including higher harmonics, as well as their post-Newtonian amplitude corrections, in the template gravitational waveforms employed in the process of parameter estimation using matched filtering. We consider the bounds that could be achieved using advanced LIGO, a proposed third generation instrument called Einstein Telescope, and the proposed space interferometer LISA. We find that in all cases, the bounds on the graviton Compton wavelength are improved by almost an order of magnitude for higher masses when amplitude corrections are included.

by Hughes, Scott A.
90 pages, 12 figures. Invited review to appear in Annual Reviews of Astronomy and Astrophysics. Further minor tweaks in response to reader feedback

Largely motivated by the development of highly sensitive gravitational-wave detectors, our understanding of merging compact binaries and the gravitational waves they generate has improved dramatically in recent years. Breakthroughs in numerical relativity now allow us to model the coalescence of two black holes with no approximations or simplifications. There has also been outstanding progress in our analytical understanding of binaries. We review these developments, examining merging binaries using black hole perturbation theory, post-Newtonian expansions, and direct numerical integration of the field equations. We summarize these approaches and what they have taught us about gravitational waves from compact binaries. We place these results in the context of gravitational-wave generating systems, analyzing the impact gravitational wave emission has on their sources, as well as what we can learn about them from direct gravitational-wave measurements.

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.