## [1003.4993] Relativistic Suppression of Black Hole Recoils

Authors: Michael Kesden, Ulrich Sperhake, Emanuele Berti

Date: 25 Mar 2010

Abstract: 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.

#### Mar 31, 2010

1003.4993 (/preprints)
2010-03-31, 14:50 

## [1003.5122] Symplectic Integration of Post-Newtonian Equations of Motion with Spin

Authors: Christian Lubich, Benny Walther, Bernd Bruegmann

Date: 26 Mar 2010

Abstract: 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.

#### Mar 31, 2010

1003.5122 (/preprints)
2010-03-31, 14:50 

## [1003.5143] The Einstein-Maxwell-Particle System: II) The Weak Field Approximation in the 3-Orthogonal Gauges and Hamiltonian Post-Minkowskian Gravity: the N-Body Problem and Gravitational Waves with Asymptotic Background

Authors: David Alba, Luca Lusanna

Date: 26 Mar 2010

Abstract: In this second paper we define a Post-Minkowskian weak field approximation leading to a linearization of the Hamilton equations of ADM tetrad gravity in the York canonical basis in a family of non-harmonic 3-orthogonal Schwinger time gauges. The York time ${}ˆ3K$ (the relativistic inertial gauge variable, not existing in Newtonian gravity, parametrizing the family and connected to the freedom in clock synchronization, i.e. to the definition of the instantaneous 3-spaces) is put equal to an arbitrary numerical function. The matter are point particles, with a Grassmann regularization of self-energies, and the electro-magnetic field in the radiation gauge: a ultraviolet cutoff allows a consistent linearization, which is shown to be the lowest order of a Hamiltonian Post-Minkowskian (HPM) expansion. We solve the constraints and the Hamilton equations for the tidal variables and we find Post-Minkowskian gravitational waves with asymptotic background (and the correct quadrupole emission formula) propagating on dynamically determined non-Euclidean 3-spaces. The conserved ADM energy and the Grassmann regularizzation of self-energies imply the correct energy balance. Then a Post-Newtonian (PN) expansion at all orders of HPM can be done by adding suitable slow motion conditions.
The dependence on the York time of the equations of motion of the particles and of quantities like the redshift and the luminosity distance is explicitly given. As a consequence of a discussion on the {\it gauge problem in general relativity}, it turns out that there is the possibility that at least part of dark matter could be explained as a relativistic inertial effect at the 0.5PN order induced by the York time.

#### Mar 31, 2010

1003.5143 (/preprints)
2010-03-31, 14:50 

## [1003.5528] Modulation of LISA free-fall orbits due to the Earth-Moon system

Authors: M. Cerdonio, F. De Marchi, R. De Pietri, P. Jetzer, F. Marzari, G. Mazzolo, A. Ortolan, M. Sereno

Date: 29 Mar 2010

Abstract: We calculate the effect of the Earth-Moon (EM) system on the free-fall motion of LISA test masses. We show that the periodic gravitational pulling of the EM system induces a resonance with fundamental frequency 1 yrˆ-1 and a series of periodic perturbations with frequencies equal to integer harmonics of the synodic month (9.92 10ˆ-7 Hz). We then evaluate the effects of these perturbations (up to the 6th harmonics) on the relative motions between each test masses couple, finding that they range between 3mm and 10pm for the 2nd and 6th harmonic, respectively. If we take the LISA sensitivity curve, as extrapolated down to 10ˆ-6 Hz, we obtain that a few harmonics of the EM system can be detected in the Doppler data collected by the LISA space mission. This suggests that the EM system gravitational near field could provide an absolute calibration for the LISA sensitivity at very low frequencies.

#### Mar 31, 2010

1003.5528 (/preprints)
2010-03-31, 14:49 

## [1003.5553] Gravitational Waves Notes, Issue #2 : "A probe of spacetime and astrophysics: EMRIs"

Authors: Pau Amaro-Seoane, Bernard Schutz, Nicolas Yunes

Date: 29 Mar 2010

Abstract: GW Notes was born from the need for a journal where the distinct communities involved in gravitation wave research might gather. While these three communities - Astrophysics, General Relativity and Data Analysis - have made significant collaborative progress over recent years, we believe that it is indispensable to future advancement that they draw closer, and that they speak a common idiom. For this GW Notes issue we have approached Nicolás Yunes (Princeton University) to extend in high detail his recent work on EMRI waveforms for our highlight article.

#### Mar 31, 2010

1003.5553 (/preprints)
2010-03-31, 14:49 

## [1003.4851] Circular inspiral templates

Authors: Manuel Tessmer

Date: 25 Mar 2010

Abstract: Recently, a new class of restricted gravitational wave search templates, termed the TaylorEt template was proposed for the search of inspiralling compact binaries. The TaylorEt approximant is different from the usual time-domain post-Newtonian approximants in that it employs the orbital binding energy rather than the orbital frequency or the closely related parameter "x". We perform detailed studies to probe the fitting factors of TaylorEt at 3.5pN for nonspinning comparable mass compact binaries vis-a-vis the TaylorT1, TaylorT4, and TaylorF2 at 3.5pN approximants in LIGO, Advanced LIGO and Virgo interferometers.

#### Mar 26, 2010

1003.4851 (/preprints)
2010-03-26, 17:09 

## [1003.4946] Perfect porcupines: ideal networks for low frequency gravitational wave astronomy

Authors: Latham Boyle

Date: 25 Mar 2010

Abstract: Perfect porcupines are specially-configured networks of gravitational wave detectors, in the limit that the individual detectors and the distances between them are short relative to the gravitational wavelengths of interest. They have beautiful properties which make them ideal gravitational wave telescopes. I present the most important cases explicitly. For a network of one-arm detectors (like "AGIS" \cite{Dimopoulos:2008sv}), the minimal perfect porcupine has 6 detectors, oriented along the 6 diameters of a regular icosahedron. For a network of two-arm detectors (like the equal-arm Michelson interferometers LIGO/VIRGO) the minimal perfect porcupine is a certain 5 detector configuration.

#### Mar 26, 2010

1003.4946 (/preprints)
2010-03-26, 17:08 

## [1003.4218] Gravitational wave detection with single-laser atom interferometers

Authors: Nan Yu, Massimo Tinto

Date: 22 Mar 2010

Abstract: We present a new general design approach of a broad-band detector of gravitational radiation that relies on two atom interferometers separated by a distance L. In this scheme, only one arm and one laser will be used for operating the two atom interferometers. We consider atoms in the atom interferometers not only as perfect inertial reference sensors, but also as highly stable clocks. Atomic coherence is intrinsically stable and can be many orders of magnitude more stable than a laser. The unique one-laser configuration allows us to then apply time-delay interferometry to the responses of the two atom interferometers, thereby canceling the laser phase fluctuations while preserving the gravitational wave signal in the resulting data set. Our approach appears very promising. We plan to investigate further its practicality and detailed sensitivity analysis.

#### Mar 23, 2010

1003.4218 (/preprints)
2010-03-23, 15:02 

## [1003.3865] A General Formula for Black Hole Gravitational Wave Kicks

Authors: James R. van Meter, M. Coleman Miller, John G. Baker, William D. Boggs, Bernard J. Kelly

Date: 19 Mar 2010

Abstract: 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.

#### Mar 22, 2010

1003.3865 (/preprints)
2010-03-22, 14:52 

## [1003.3415] Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: I. Properties of a Quasi-Kerr Spacetime

Authors: Tim Johannsen (Arizona), Dimitrios Psaltis (Arizona)

Date: 17 Mar 2010

Abstract: According to the no-hair theorem, an astrophysical black hole is uniquely described by only two quantities, the mass and the spin. In this series of papers, we investigate a framework for testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. We formulate our approach in terms of a parametric spacetime which contains a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation of the black-hole quadrupole moment from its Kerr value has to be zero. We analyze in detail the properties of this quasi-Kerr spacetime that are critical to interpreting observations of black holes and demonstrate their dependence on the spin and quadrupole moment. In particular, we show that the location of the innermost stable circular orbit and the gravitational lensing experienced by photons are affected significantly at even modest deviations of the quadrupole moment from the value predicted by the no-hair theorem. We argue that observations of black-hole images, of relativistically broadened iron lines, as well as of thermal X-ray spectra from accreting black holes will lead in the near future to an experimental test of the no-hair theorem.

#### Mar 22, 2010

1003.3415 (/preprints)
2010-03-22, 14:52 

## [1003.3701] B-mode polarization induced by gravitational waves from kinks on infinite cosmic strings

Authors: Masahiro Kawasaki, Koichi Miyamoto, Kazunori Nakayama

Date: 19 Mar 2010

Abstract: We investigate the effect of the stochastic gravitational wave (GW) background produced by kinks on infinite cosmic strings, whose spectrum was derived in our previous work, on the B-mode power spectrum of the cosmic microwave background (CMB) anisotropy. We find that the B-mode polarization due to kinks is comparable to that induced by the motion of the string network and hence the contribution of GWs from kinks is important for estimating the B-mode power spectrum originating from cosmic strings. If the tension of cosmic strings \mu is large enough i.e., G\mu >~ 10ˆ{-8}, B-mode polarization induced by cosmic strings can be detected by future CMB experiments.

#### Mar 22, 2010

1003.3701 (/preprints)
2010-03-22, 14:52 

## [1003.2939] A tapering window for time-domain templates and simulated signals in the detection of gravitational waves from coalescing compact binaries

Authors: D.J.A. McKechan, C. Robinson, B.S. Sathyaprakash

Date: 15 Mar 2010

Abstract: Inspiral signals from binary black holes, in particular those with masses in the range $10M_\odot \lsim M \lsim 1000 M_\odot,$ may last for only a few cycles within a detector's most sensitive frequency band. The spectrum of a square-windowed time-domain signal could contain unwanted power that can cause problems in gravitational wave data analysis, particularly when the waveforms are of short duration. There may be leakage of power into frequency bins where no such power is expected, causing an excess of false alarms. We present a method of tapering the time-domain waveforms that significantly reduces unwanted leakage of power, leading to a spectrum that agrees very well with that of a long duration signal. Our tapered window also decreases the false alarms caused by instrumental and environmental transients that are picked up by templates with spurious signal power. The suppression of background is an important goal in noise-dominated searches and can lead to an improvement in the detection efficiency of the search algorithms.

#### Mar 17, 2010

1003.2939 (/preprints)
2010-03-17, 12:10 

## [1003.2735] Eccentric orbital motion of compact binaries with aligned spins and angular momentum under higher order spin coupling

Authors: Manuel Tessmer, Johannes Hartung, Gerhard Schaefer

Date: 13 Mar 2010

Abstract: 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.

#### Mar 17, 2010

1003.2735 (/preprints)
2010-03-17, 12:10 

## [1003.2481] Sensitivity to Gravitational Waves from Compact Binary Coalescences Achieved during LIGO's Fifth and Virgo's First Science Run

Authors: LIGO Scientific Collaboration, Virgo Collaboration

Date: 12 Mar 2010

Abstract: We summarize the sensitivity achieved by the LIGO and Virgo gravitational wave detectors for compact binary coalescence (CBC) searches during LIGO's fifth science run and Virgo's first science run. We present noise spectral density curves for each of the four detectors that operated during these science runs which are representative of the typical performance achieved by the detectors for CBC searches. These spectra are intended for release to the public as a summary of detector performance for CBC searches during these science runs.

#### Mar 17, 2010

1003.2481 (/preprints)
2010-03-17, 12:10 

## [1003.3120] An observable signature of a background deviating from Kerr

Authors: Georgios Lukes-Gerakopoulos, Theocharis A. Apostolatos, George Contopoulos

Date: 16 Mar 2010

Abstract: By detecting gravitational wave signals from extreme mass ratio inspiraling sources (EMRIs) we will be given the opportunity to check our theoretical expectations regarding the nature of supermassive bodies that inhabit the central regions of galaxies. We have explored some qualitatively new features that a perturbed Kerr metric induces in its geodesic orbits. Since a generic perturbed Kerr metric does not possess all the special symmetries of a Kerr metric, the geodesic equations in the former case are described by a slightly nonintegrable Hamiltonian system. According to the Poincar\'{e}-Birkhoff theorem this causes the appearance of the so-called Birkhoff chains of islands on the corresponding surfaces of section in between the anticipated KAM curves of the integrable Kerr case, whenever the intrinsic frequencies of the system are at resonance. The chains of islands are characterized by finite width, i.e. there is a finite range of initial conditions that correspond to a particular resonance and consequently to a constant rational ratio of intrinsic frequencies. Thus while the EMRI changes adiabatically by radiating energy and angular momentum, by monitoring the frequencies of a signal we can look for a transient pattern, in the form of a plateau, in the evolution of their ratio. We have shown that such a plateau is anticipated to be apparent in a quite large fraction of possible orbital characteristics if the central gravitating source is not a Kerr black hole. Moreover the plateau in the ratio of frequencies is expected to be more prominent at specific rational values that correspond to the strongest resonances. This gives a possible observational detection of such non-Kerr exotic objects.

#### Mar 17, 2010

1003.3120 (/preprints)
2010-03-17, 12:10 

## [1003.2480] Predictions for the Rates of Compact Binary Coalescences Observable by Ground-based Gravitational-wave Detectors

Date: 12 Mar 2010

Abstract: We present an up-to-date, comprehensive summary of the rates for all types of compact binary coalescence sources detectable by the Initial and Advanced versions of the ground-based gravitational-wave detectors LIGO and Virgo. Astrophysical estimates for compact-binary coalescence rates depend on a number of assumptions and unknown model parameters, and are still uncertain. The most confident among these estimates are the rate predictions for coalescing binary neutron stars which are based on extrapolations from observed binary pulsars in our Galaxy. These yield a likely coalescence rate of 100 per Myr per Milky Way Equivalent Galaxy (MWEG), although the rate could plausibly range from 1 per Myr per MWEG to 1000 per Myr per MWEG. We convert coalescence rates into detection rates based on data from the LIGO S5 and Virgo VSR2 science runs and projected sensitivities for our Advanced detectors. Using the detector sensitivities derived from these data, we find a likely detection rate of 0.02 per year for Initial LIGO-Virgo interferometers, with a plausible range between 0.0002 and 0.2 per year. The likely binary neutron-star detection rate for the Advanced LIGO-Virgo network increases to 40 events per year, with a range between 0.4 and 400 per year.

#### Mar 17, 2010

1003.2480 (/preprints)
2010-03-17, 12:10 

## [1003.2504] Geometrical Expression for the Angular Resolution of a Network of Gravitational-Wave Detectors

Authors: Linqing Wen, Yanbei Chen

Date: 12 Mar 2010

Abstract: We report for the first time general geometrical expressions for the angular resolution of an arbitrary network of interferometric gravitational-wave (GW) detectors when the arrival-time of a GW is unknown. We show explicitly elements that decide the angular resolution of a GW detector network. In particular, we show the dependence of the angular resolution on areas formed by projections of pairs of detectors and how they are weighted by sensitivities of individual detectors. Numerical simulations are used to demonstrate the capabilities of the current GW detector network. We confirm that the angular resolution is poor along the plane formed by current LIGO-Virgo detectors. A factor of a few to more than ten fold improvement of the angular resolution can be achieved if the proposed new GW detectors LCGT or AIGO are added to the network. We also discuss the implications of our results for the design of a GW detector network, optimal localization methods for a given network, and electromagnetic follow-up observations.

#### Mar 17, 2010

1003.2504 (/preprints)
2010-03-17, 12:09 

## [1003.2178] On blind searches for noise dominated signals: a loosely coherent approach

Date: 10 Mar 2010

Abstract: We introduce a "loosely coherent" method for detection of continuous gravitational waves that bridges the gap between semi-coherent and purely coherent methods. Explicit control over accepted families of signals is used to increase sensitivity of power-based statistic while avoiding the high computational costs of conventional matched filters. Several examples as well as a prototype implementation are discussed.

#### Mar 10, 2010

1003.2178 (/preprints)
2010-03-10, 21:10 

## [1003.2169] The (Double) White Dwarf Binary SDSS 1257 5428

Authors: S. R. Kulkarni (Caltech), M. H. van Kerkwijk (Caltech, Toronto)

Date: 10 Mar 2010

Abstract: SDSS 1257+5428 is a white dwarf in a close orbit with a companion that has been suggested to be a neutron star. If so, it hosts the closest known neutron star, and its existence implies a great abundance of similar systems and a rate of white-dwarf neutron-star mergers similar to that of the type Ia supernova rate. Here, we present high signal-to-noise spectra of SDSS 1257+5428, which confirm an independent finding that the system is in fact composed of two white dwarfs, one relatively cool and with low mass, and the other hotter and more massive. With this, the demographics and merger rate are no longer puzzling (various factors combine to lower the latter by more than two orders of magnitude). We show that the spectra are fit well with a combination of two hydrogen model atmospheres, as long as the lines of the higher-gravity component are broadened significantly relative to what is expected from just pressure broadening. Interpreting this additional broadening as due to rotation, the inferred spin period is short, about 1 minute. Similarly rapid rotation is only seen in accreting white dwarfs that are magnetic; empirically, it appears that in non-magnetized white dwarfs, accreted angular momentum is lost by nova explosions before it can be transferred to the white dwarf. This suggests that the massive white dwarf in SDSS 1257+5428 is magnetic as well, with B~10ˆ5 G. Alternatively, the broadening seen in the spectral lines could be due to a stronger magnetic field, of ~10ˆ6 G. The two models could be distinguished by further observations.

#### Mar 10, 2010

1003.2169 (/preprints)
2010-03-10, 21:09 

## [1003.1735] Probing the Gravitational Wave Signature from Cosmic Phase Transitions at Different Scales

Authors: Lawrence M. Krauss (1), Katherine Jones-Smith (2), Harsh Mathur (2), James Dent (1) ((1) Arizona State University (2) Case Western Reserve University)

Date: 8 Mar 2010

Abstract: We present a new signature by which to one could potentially discriminate between a spectrum of gravitational radiation generated by a self-ordering scalar field vs that of inflation, specifically a comparison of the magnitude of a flat spectrum at frequencies probed by future direct detection experiments to the magnitude of a possible polarization signal in the Cosmic Microwave Background (CMB) radiation. In the process we clarify several issues related to the proper calculation of such modes, focusing on the effect of post-horizon-crossing evolution.

#### Mar 10, 2010

1003.1735 (/preprints)
2010-03-10, 21:09 

## [1003.2185] Confirmation of general relativity on large scales from weak lensing and galaxy velocities

Authors: Reinabelle Reyes, Rachel Mandelbaum, Uros Seljak, Tobias Baldauf, James E. Gunn, Lucas Lombriser, Robert E. Smith

Date: 10 Mar 2010

Abstract: Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, EG, that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to 'galaxy bias' (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of EG different from the general relativistic prediction because, in these theories, the 'gravitational slip' (the difference between the two potentials that describe perturbations in the gravitational metric) is non-zero, which leads to changes in the growth of structure and the strength of the gravitational lensing effect3. Here we report that EG = 0.39 +/- 0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of EG $\approx$ 0.4. The measured value excludes a model within the tensor-vector-scalar gravity theory, which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f(R) theory, which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.

#### Mar 10, 2010

1003.2185 (/preprints)
2010-03-10, 21:09 

## [1003.0882] Ultra-relativistic grazing collisions of black holes

Authors: U.Sperhake, V.Cardoso, F.Pretorius, E.Berti, T.Hinderer, N.Yunes

Date: 3 Mar 2010

Abstract: We study gravitational wave emission, zoom-whirl behavior and the resulting spin of the remnant black hole in highly boosted collisions of equal-mass, non spinning black-hole binaries with generic impact parameter.

#### Mar 03, 2010

1003.0882 (/preprints)
2010-03-03, 22:11 

## [1003.0485] Binary black hole merger gravitational waves and recoil in the large mass ratio limit

Authors: Pranesh A. Sundararajan, Gaurav Khanna, Scott A. Hughes

Date: 2 Mar 2010

Abstract: Spectacular breakthroughs in numerical relativity now make it possible to compute spacetime dynamics in almost complete generality, allowing us to model the coalescence and merger of binary black holes with essentially no approximations. The primary limitation of these calculations is now computational. In particular, it is difficult to model systems with large mass ratio and large spins, since one must accurately resolve the multiple lengthscales which play a role in such systems. Perturbation theory can play an important role in extending the reach of computational modeling for binary systems. In this paper, we present first results of a code which allows us to model the gravitational waves generated by the inspiral, merger, and ringdown of a binary system in which one member of the binary is much more massive than the other. This allows us to accurately calibrate binary dynamics in the large mass ratio regime. We focus in this analysis on the recoil imparted to the merged remnant by these waves. We closely examine the "antikick", an anti-phase cancellation of the recoil arising from the plunge and ringdown waves, described in detail by Schnittman et al. We find that, for orbits aligned with the black hole spin, the antikick grows as a function of spin. The total recoil is smallest for prograde coalescence into a rapidly rotating black hole, and largest for retrograde coalescence. Amusingly, this completely reverses the predicted trend for kick versus spin from analyses that only include inspiral information.

#### Mar 02, 2010

1003.0485 (/preprints)
2010-03-02, 21:32 

## [1003.0390] Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order

Authors: Tilman J. Rothe, Gerhard Sch&#xe4;fer

Date: 1 Mar 2010

Abstract: 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.

#### Mar 02, 2010

1003.0390 (/preprints)
2010-03-02, 21:31 

## [1003.0597] Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis

Authors: Sebastiano Bernuzzi, Alessandro Nagar

Date: 2 Mar 2010

Abstract: Building up on previous work, we present a new calculation of the gravitational wave (GW) emission generated during the transition from quasi-circular inspiral to plunge, merger and ringdown by a binary system of nonspinning black holes, of masses $m_1$ and $m_2$, in the extreme mass ratio limit, $m_1 m_2\ll(m_1+m_2)ˆ2$. The relative dynamics of the system is computed {\it without making any adiabatic approximation} by using an effective one body (EOB) description, namely by representing the binary by an effective particle of mass $\mu=m_1 m_2/(m_1+m_2)$ moving in a (quasi-)Schwarzschild background of mass $M=m_1+m_2$ and submitted to an $\O(\nu)$ 5PN-resummed analytical radiation reaction force, with $\nu=\mu/M$. The gravitational wave emission is calculated via a multipolar Regge-Wheeler-Zerilli type perturbative approach (valid in the limit $\nu\ll 1$). We consider three mass ratios, $\nu={10ˆ{-2},10ˆ{-3},10ˆ{-4}}$,and we compute the multipolar waveform up to $\ell=8$. We estimate energy and angular momentum losses during the quasi-universal and quasi-geodesic part of the plunge phase and we analyze the structure of the ringdown. We calculate the gravitational recoil, or "kick", imparted to the merger remnant by the gravitational wave emission and we emphasize the importance of higher multipoles to get a final value of the recoil $v/(c\nuˆ2)=0.0446$. We finally show that there is an {\it excellent fractional agreement} ($\sim 10ˆ{-3}$) (even during the plunge) between the 5PN EOB analytically-resummed radiation reaction flux and the numerically computed gravitational wave angular momentum flux. This is a further confirmation of the aptitude of the EOB formalism to accurately model extreme-mass-ratio inspirals, as needed for the future space-based LISA gravitational wave detector.

#### Mar 02, 2010

1003.0597 (/preprints)
2010-03-02, 21:31