by Burko, Lior M. and Hughes, Scott A.
5 pages, no figures, submitted to Phys. Rev. D

The goal of much research in relativity is to understand gravitational waves generated by a strong-field dynamical spacetime. Quantities of particular interest for many calculations are the Weyl scalar $latex \psi_4$, which is simply related to the flux of gravitational waves far from the source, and the flux of energy carried to distant observers, $latex \dot E$. Conservation laws guarantee that, in asympotically flat spacetimes, $latex \psi_4 \propto 1/r$ and $latex \dot E \propto 1/r^2$ as $latex r \to \infty$. Most calculations extract these quantities at some finite extraction radius. An understanding of finite radius corrections to $latex \psi_4$ and $latex \dot E$ allows us to more accurately infer their asymptotic values from a computation. In this paper, we show that, if the final state of the system is a black hole, then the leading correction to $latex \psi_4$ is $latex {\cal O}(1/r^3)$, and that to the energy flux is $latex {\cal O}(1/r^4)$ — not $latex {\cal O}(1/r^2)$ and $latex {\cal O}(1/r^3)$ as one might naively guess. Our argument only relies on the behavior of the curvature scalars for black hole spacetimes. Using black hole perturbation theory, we calculate the corrections to the leading falloff, showing that it is quite easy to correct for finite extraction radius effects.

by Komorowski, P. G. and Valluri, S. R. and Houde, M.
48 pages, 7 figures, submitted to Classical and Quantum Gravity on March 2nd, 2010

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits; and develop an analysis that is independent of and complements radiation reaction models. For a Schwarzschild black hole, the polar orbits represent the abutment between the prograde and retrograde orbits at which Q is at its maximum value for given values of latus rectum (l) and eccentricity (e). The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or abutment, to be moved towards greater orbital inclination; thus it no longer cleanly separates prograde and retrograde orbits. To characterise the abutment of a Kerr black hole (KBH), we first investigated the last stable orbit (LSO) of a test-particle about a KBH, and then extended this work to general orbits. To develop a better understanding of the evolution of Q we developed analytical formulae for Q in terms of l, e, and S to describe elliptical orbits at the abutment, polar orbits, and last stable orbits (LSO). By knowing the analytical form of dQ/dl at the abutment, we were able to test a 2PN flux equation for Q. We also used these formulae to numerically calculate the di/dl of hypothetical circular orbits that evolve along the abutment. From these values we have determined that di/dl = -(122.7S – 36S^3)l^-11/2 -(63/2 S + 35/4 S^3) l^-9/2 -15/2 S l^-7/2 -9/2 S l^-5/2. Thus the abutment becomes an important analytical and numerical laboratory for studying the evolution of Q and i in Kerr spacetime and for testing current and future radiation back-reaction models for near-polar retrograde orbits.

by Colaiuda, A. and Ferrari, V. and Gualtieri, L. and Pons, J. A.
25 pages, 9 figures, submitted to MNRAS

We find numerical solutions of the coupled system of Einstein-Maxwell’s equations with a linear approach, in which the magnetic field acts as a perturbation of a spherical neutron star. In our study, magnetic fields having both poloidal and toroidal components are considered, and higher order multipoles are also included. We evaluate the deformations induced by different field configurations, paying special attention to those for which the star has a prolate shape. We also explore the dependence of the stellar deformation on the particular choice of the equation of state and on the mass of the star. Our results show that, for neutron stars with mass M = 1.4 Msun and surface magnetic fields of the order of 10^15 G, a quadrupole ellipticity of the order of 10^(-6) – 10^(-5) should be expected. Low mass neutron stars are in principle subject to larger deformations (quadrupole ellipticities up to 10^(-3) in the most extreme case). The effect of quadrupolar magnetic fields is comparable to that of dipolar components. A magnetic field permeating the whole star is normally needed to obtain negative quadrupole ellipticities, while fields confined to the crust typically produce positive quadrupole ellipticities.

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 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 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 Sopuerta, Carlos F. and Yunes, Nicolas
3 pages. To appear in Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, edited by Thibault Damour, Robert T Jantzen and Remo Ruffini, World Scientific, Singapore, 2010

The inspiral of stellar compact objects into massive black holes, usually known as extreme-mass-ratio inspirals (EMRIs), is one of the most important sources of gravitational-waves for the future Laser Interferometer Space Antenna (LISA). Intermediate-mass-ratio inspirals (IMRIs are also of interest to advance ground-based gravitational-wave observatories. We discuss here how modifications to the gravitational interaction can affect the signals emitted by these systems and their detectability by LISA. We concentrate in particular on Chern-Simons modified gravity, a theory that emerges in different quantum gravitational approaches.

by Canizares, Priscilla and Sopuerta, Carlos F.
3 pages. To appear in Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, edited by Thibault Damour, Robert T Jantzen and Remo Ruffini, World Scientific, Singapore, 2010

We introduce a new time-domain method for computing the self-force acting on a scalar particle in a Schwarzschild geometry. The principal feature of our method consists in the division of the spatial domain into several subdomains and locating the particle at the interface betweem two them. In this way, we avoid the need of resolving a small length scale associated with the presence of a particle in the computational domain and, at the same time, we avoid numerical problems due to the low differentiability of solutions of equations with point-like singular behaviour.

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 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 McWilliams, Sean T. and Thorpe, James Ira and Baker, John G. and Kelly, Bernard J.
16 pages, 9 figures, submitted to Phys. Rev. D

We investigate the precision with which the parameters describing the characteristics and location of nonspinning black hole binaries can be measured with the Laser Interferometer Space Antenna (LISA). By using complete waveforms including the inspiral, merger and ringdown portions of the signals, we find that LISA will have far greater precision than previous estimates for nonspinning mergers that ignored the merger and ringdown. Our analysis covers nonspinning waveforms with moderate mass ratios, q >= 1/10, and total masses 10^5 < M/M_{Sun} < 10^7. We compare the parameter uncertainties using the Fisher matrix formalism, and establish the significance of mass asymmetry and higher-order content to the predicted parameter uncertainties resulting from inclusion of the merger. In real-time observations, the later parts of the signal lead to significant improvements in sky-position precision in the last hours and even the final minutes of observation. For comparable mass systems with total mass M/M_{Sun} = ~10^6, we find that the increased precision resulting from including the merger is comparable to the increase in signal-to-noise ratio. For the most precise systems under investigation, half can be localized to within O(10 arcmin), and 10% can be localized to within O(1 arcmin).

by Lousto, Carlos O. and Nakano, Hiroyuki and Zlochower, Yosef and Campanelli, Manuela
20 pages, 24 figures, abridged abstract

We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions S1 and S2 and magnitudes S1=S2=0.97 for different mass ratios. Starting from a fiducial initial separation of ri=50m, we perform 3.5PN evolutions down to rf=5m. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, L. We perform 16^4 simulations for six mass ratios between q=1 and q=1/16 and compute the distribution of the angles between L and Delta and L and S, directly related to recoil velocities and total angular momentum. We find a small but statistically significant bias of the distribution towards counter-alignment of both scalar products. To study the merger of black-hole binaries, we turn to full numerical techniques. We introduce empirical formulae to describe the final remnant black hole mass, spin, and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins. We then evaluate those formulae for randomly chosen directions of the individual spins and magnitudes as well as the binary’s mass ratio. We found that the magnitude of the recoil velocity distribution decays as P(v) \exp(-v/2500km/s), =630km/s, and sqrt{ – ^2}= 534km/s, leading to a 23% probability of recoils larger than 1000km/s, and a highly peaked angular distribution along the final orbital axis. The final black-hole spin magnitude show a universal distribution highly peaked at Sf/mf^2=0.73 and a 25 degrees misalignment with respect to the final orbital angular momentum.

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 Spallicci, A. and Aoudia, S.
To be published on 21 Rencontres de Blois: Windows on the Universe, http://confs.obspm.fr/Blois2009/, 4 pages 1 figure

Through detection by low gravitational wave space interferometers, the capture of stars by supermassive black holes will constitute a giant step forward in the understanding of gravitation in strong field. The impact of the perturbations on the motion of the star is computed via the tail, the back-scattered part of the perturbations, or via a radiative Green function. In the former approach, the self-force acts upon the background geodesic, while in the latter, the geodesic is conceived in the total (background plus perturbations) field. Regularisations (mode-sum and Riemann-Hurwitz $latex \zeta$ function) intervene to cancel divergencies coming from the infinitesimal size of the particle. The non-adiabatic trajectories require the most sophisticated techniques for studying the evolution of the motion, like the self-consistent approach.

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 Szilágyi, Béla and Lindblom, Lee and Scheel, Mark A.
16 pages, 16 figures

Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of “generic” binary black-hole evolutions using the pseudo-spectral evolution code SpEC. These improvements include the use of a new damped-wave gauge condition, a new grid structure with appropriate filtering that improves stability, and better adaptivity in conforming the grid structures to the shapes and sizes of the black holes. Simulations illustrating the success of these new methods are presented for a variety of binary black-hole systems. These include fairly “generic” systems with unequal masses (up to 2:1 mass ratios), and spins (with magnitudes up to 0.4 M^2) pointing in various directions.

by Yunes, Nicolas and Pretorius, Frans
25 pages, submitted to Phys. Rev. D

We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid in the weak-field, as verified by precision experiments and observations, but it need not hold in the dynamical strong-field regime where tests are lacking. Fundamental bias can cause systematic errors in the detection and parameter estimation of signals, which can lead to a mischaracterization of the universe through incorrect inferences about source event rates and populations. We propose a remedy through the introduction of the parameterized post-Einsteinian framework, which consists of the enhancement of waveform templates via the inclusion of post-Einsteinian parameters. These parameters would ostensibly be designed to interpolate between templates constructed in general relativity and well-motivated alternative theories of gravity, and also include extrapolations that follow sound theoretical principles, such as consistency with conservation laws and symmetries. As an example, we construct parameterized post-Einsteinian templates for the binary coalescence of equal-mass, non-spinning compact objects in a quasi-circular inspiral. The parametrized post-Einsteinian framework should allow matched filtered data to select a specific set of post-Einsteinian parameters without a priori assuming the validity of the former, thus either verifying general relativity or pointing to possible dynamical strong-field deviations.

by Capozziello, S. and De Laurentis, M. and Forte, L. and Garufi, F. and Milano, L.
14 pages, 7 figures

Gravitational waveforms and production could be considerably affected by gravitomagnetic corrections considered in relativistic theory of orbits. Beside the standard periastron effect of General Relativity, new nutation effects come out when c^{-3} corrections are taken into account. Such corrections emerge as soon as matter-current densities and vector gravitational potentials cannot be discarded into dynamics. We study the gravitational waves emitted through the capture, in the gravitational field of massive binary systems (e.g. a very massive black hole on which a stellar object is inspiralling) via the quadrupole approximation, considering precession and nutation effects. We present a numerical study to obtain the gravitational wave luminosity, the total energy output and the gravitational radiation amplitude. From a crude estimate of the expected number of events towards peculiar targets (e.g. globular clusters) and in particular, the rate of events per year for dense stellar clusters at the Galactic Center (SgrA*), we conclude that this type of capture could give signatures to be revealed by interferometric GW antennas, in particular by the forthcoming laser interferometer space antenna LISA.

by Comeau, Simon and Poisson, Eric
4 pages, 2 figures

The rates at which the mass and angular momentum of a small black hole change as a result of a tidal interaction with a much larger black hole are calculated to leading order in the small mass ratio. The small black hole is either rotating or nonrotating, and it moves on a circular orbit in the equatorial plane of the large Kerr black hole. The orbits are fully relativistic, and the rates are computed to all orders in the orbital velocity V < V_{isco}, which is limited only by the size of the innermost stable circular orbit. We show that as V \to V_{isco}, the rates take on a limiting value that depends only on V_{isco} and not on the spin parameter of the large black hole.

by Detweiler, Steven
38 pages, 4 figures, Lecture given at the “School on Mass” (Orleans, France, June 2008), uses Springer’s “svmult.cls”

The gravitational field of a particle of small mass $latex \mu$ moving through curved spacetime, with metric $latex g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $latex O(\mu)$. One part is an inhomogeneous field $latex h^S_{ab}$ which, near the particle, looks like the Coulomb $latex \mu/r$ field with tidal distortion from the local Riemann tensor. This singular field is defined in a neighborhood of the small particle and does not depend upon boundary conditions or upon the behavior of the source in either the past or the future. The other part is a homogeneous field $latex h^R_{ab}$. In a perturbative analysis, the motion of the particle is then best described as being a geodesic in the metric $latex g_{ab}+h^R_{ab}$. This geodesic motion includes all of the effects which might be called radiation reaction and conservative effects as well.

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 Depies, Matthew R
129 pages, 18 figures, PhD dissertation

Gravitational wave signatures from cosmic strings are analyzed numerically. Cosmic string networks form during phase transistions in the early universe and these networks of long cosmic strings break into loops that radiate energy in the form of gravitational waves until they decay. The gravitational waves come in the form of harmonic modes from individual string loops, a “confusion noise” from galactic loops, and a stochastic background of gravitational waves from a network of loops. In this study string loops of larger size $latex \alpha$ and lower string tensions $latex G\mu$ (where $latex \mu$ is the mass per unit length of the string) are investigated than in previous studies. Several detectors are currently searching for gravitational waves and a space based satellite, the Laser Interferometer Space Antenna (LISA), is in the final stages of pre-flight. The results for large loop sizes ($latex \alpha=0.1$) put an upper limit of about $latex G\mu<10^{-9}$ and indicate that gravitational waves from string loops down to $latex G\mu \approx 10^{-20}$ could be detectabe by LISA. The string tension is related to the energy scale of the phase transition and the Planck mass via $latex G\mu = \Lambda_s^2 / m_{pl}^2$, so the limits on $latex G\mu$ set the energy scale of any phase transition to $latex \Lambda_s < 10^{-4.5} m_{pl}$. Our results indicate that loops may form a significant gravitational wave signal, even for string tensions too low to have larger cosmological effects.

by Valtonen, M. J. and Mikkola, S. and Merritt, D. and Gopakumar, A. and Lehto, H. J. and Hyvönen, T. and Rampadarath, H. and Saunders, R. and Basta, M. and Hudec, R.
9 pages, 6 figures, IAU261: Relativity in Fundamental Astronomy

Supermassive black holes are common in centers of galaxies. Among the active galaxies, quasars are the most extreme, and their black hole masses range as high as to $latex 6\cdot 10^{10} M_\odot$. Binary black holes are of special interest but so far OJ287 is the only confirmed case with known orbital elements. In OJ287, the binary nature is confirmed by periodic radiation pulses. The period is twelve years with two pulses per period. The last four pulses have been correctly predicted with the accuracy of few weeks, the latest in 2007 with the accuracy of one day. This accuracy is high enough that one may test the higher order terms in the Post Newtonian approximation to General Relativity. The precession rate per period is $latex 39^\circ.1 \pm 0^\circ.1$, by far the largest rate in any known binary, and the $latex (1.83\pm 0.01)\cdot 10^{10} M_\odot$ primary is among the dozen biggest black holes known. We will discuss the various Post Newtonian terms and their effect on the orbit solution.

The over 100 year data base of optical variations in OJ287 puts limits on these terms and thus tests the ability of Einstein’s General Relativity to describe, for the first time, dynamic binary black hole spacetime in the strong field regime. The quadrupole-moment contributions to the equations of motion allows us to constrain the `no-hair’ parameter to be $latex 1.0\:\pm\:0.3$ which supports the black hole no-hair theorem within the achievable precision.

by Barack, Leor
Invited topical review for CQG; 61 pages, 4 eps figures; uses iopart.cls, iopart10.clo

This review is concerned with the gravitational self-force acting on a mass particle in orbit around a large black hole. Renewed interest in this old problem is driven by the prospects of detecting gravitational waves from strongly gravitating binaries with extreme mass ratios. We begin here with a summary of recent advances in the theory of gravitational self-interaction in curved spacetime, and proceed to survey some of the ideas and computational strategies devised for implementing this theory in the case of a particle orbiting a Kerr black hole. We review in detail two of these methods: (i) the standard mode-sum method, in which the metric perturbation is regularized mode-by-mode in a multipole decomposition, and (ii) $latex m$-mode regularization, whereby individual azimuthal modes of the metric perturbation are regularized in 2+1 dimensions. We discuss several practical issues that arise, including the choice of gauge, the numerical representation of the particle singularity, and how high-frequency contributions near the particle are dealt with in frequency-domain calculations. As an example of a full end-to-end implementation of the mode-sum method, we discuss the computation of the gravitational self-force for eccentric geodesic orbits in Schwarzschild, using a direct integration of the Lorenz-gauge perturbation equations in the time domain. With the computational framework now in place, researchers have recently turned to explore the physical consequences of the gravitational self force; we will describe some preliminary results in this area. An appendix to this review presents, for the first time, a detailed derivation of the regularization parameters necessary for implementing the mode-sum method in Kerr spacetime.

by Capozziello, S. and De Laurentis, M. and Formisano, M.
7 page, 5 figures

Gravitational waves detected from well-localized inspiraling binaries would allow to determine, directly and independently, both binary luminosity and redshift. In this case, such systems could behave as “standard candles” providing an excellent probe of cosmic distances up to $latex z <0.1$ and thus complementing other indicators of cosmological distance ladder.

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 Levin, Janna
7 pages

A spinning black hole with a much smaller black hole companion forms a fundamental gravitational system, like a colossal classical analog to an atom. In an appealing if imperfect analogy to atomic physics, this gravitational atom can be understood through a discrete spectrum of periodic orbits. Through a correspondence between the set of periodic orbits and the set of rational numbers, we are able to construct periodic tables of orbits and energy level diagrams of the accessible states around black holes. We also present a closed form expression for the rational q, thereby quantifying zoom-whirl behavior in terms of spin, energy, and angular momentum. The black hole atom is not just a theoretical construct, but corresponds to extant astrophysical systems detectable by future gravitational wave observatories.

by Asada, Hideki
21 pages, 3 figures, 1 table

Continuing work initiated in an earlier publication [Torigoe et al. Phys. Rev. Lett. {\bf 102}, 251101 (2009)], gravitational wave forms for a three-body system in Lagrange’s orbit are considered especially in an analytic method. First, we derive an expression of the three-body wave forms at the mass quadrupole, octupole and current quadrupole orders. By using the expressions, we solve a gravitational-wave {\it inverse} problem of determining the source parameters to this particular configuration (three masses, a distance of the source to an observer, and the orbital inclination angle to the line of sight) through observations of the gravitational wave forms alone. For this purpose, the chirp mass to a three-body system in the particular configuration is expressed in terms of only the mass ratios by deleting initial angle positions. We discuss also whether and how a binary source can be distinguished from a three-body system in Lagrange’s orbit or others.

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 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 Capozziello, Salvatore and De Laurentis, Mariafelicia and Forte, Luca and Garufi, Fabio and Milano, Leopoldo
6 pages, 10 figures; Multifrequency Behaviour of High-Energy Cosmic Sources, Vulcano Workshop 2009

Corrections to the relativistic theory of orbits are discussed considering higher order approximations induced by gravitomagnetic effects. Beside the standard periastron effect of General Relativity (GR), a new nutation effect was found due to the $latex {\displaystyle c^{-3}}$ orbital correction. According to the presence of that new nutation effect we studied the gravitational waveforms emitted through the capture in a gravitational field of a massive black hole (MBH) of a compact object (neutron star (NS) or BH) via the quadrupole approximation. We made a numerical study to obtain the emitted gravitational wave (GW) amplitudes. We conclude that the effects we studied could be of interest for the future space laser interferometric GW antenna LISA.

by Yagi, Kent and Tanaka, Takahiro
37 pages, 16 figures

We calculate how strong one can put constraints on the alternative theories of gravities such as Brans-Dicke and massive graviton theories with LISA. We consider the inspiral gravitational waves from NS/IMBH binaries in Brans-Dicke theory and SMBH/BH binaries in massive graviton theories. We use the 2PN waveforms including spins. We also take both precession and small eccentricity of the orbit into account. We neglect the spin of one of the binary object so that we can apply the so-called \textit{simple precession}. We perform the Monte Carlo simulations of $latex 10^4$ binaries, whose parameters include the Brans-Dicke parameter $latex \omega_{\mathrm{BD}}$ and the graviton Compton length $latex \lambda_g$. We find that including both the spin-spin coupling $latex \sigma$ and the small eccentricity into the binary parameters reduces the determination accuracy by an order of magnitude for the Brans-Dicke case, whilst it has less influence on massive graviton theories. On the other hand, including precession enhances the constraint on $latex \omega_{\mathrm{BD}}$ only 20% but it increases the constraint on $latex \lambda_g$ by several factors. For $latex (1.4+1000)M_{\odot}$ NS/BH binaries of SNR=10, one can put $latex \omega_{\mathrm{BD}}>7040$, whilst for $latex (10^7+10^6)M_{\odot}$ BH/BH binaries at 3Gpc, one can put $latex \lambda_g>4.24\times10^{21}$cm, on average. This is four orders of magnitude stronger than the one obtained from the solar system experiment. From these results, it is understood that the effects of precession and eccentricity cannot be neglected in the parameter estimation analysis.

by Stavridis, Adamantios and Will, Clifford M.
10 pages, 5 figures

Observations of gravitational waves from massive binary black hole systems at cosmological distances can be used to search for a dependence of the speed of propagation of the waves on wavelength, and thereby to bound the mass of a hypothetical graviton. We study the effects of precessions of the spins of the black holes and of the orbital angular momentum on the process of parameter estimation using matched filtering of gravitational-wave signals vs. theoretical template waveforms. For the proposed space interferometer LISA, we show that precessions, and the accompanying modulations of the gravitational waveforms, are effective in breaking degeneracies among the parameters being estimated, and effectively restore the achievable graviton-mass bounds to levels obtainable from binary inspirals without spin. For spinning, precessing binary black hole systems of equal masses (10^6 solar masses) at 3 Gpc, the bounds on the graviton Compton wavelength achievable are of the order of 5 X 10^{16} km.

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 Dai, Lixin and Fuerst, Steven V. and Blandford, Roger
16 pages, 11 figures, submitted to MNRAS; corrected typos

We present simulated results of quasi-periodic flares generated by the inelastic collisions of a star bound to a super-massive black hole (SMBH) and its attendant accretion disc. We show that the behavior of the quasi-periodicity is affected by the mass and spin of the black hole and the orbital elements of the stellar orbit. We also evaluate the possibility of extracting useful information on these parameters and verifying the character of the Kerr metric from such quasi-periodic signals. Comparisons are made with the observed optical outbursts of OJ287, infrared flares from the Galactic center and X-ray variability in RE J1034+396.

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 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 Fujita, Ryuichi and Hikida, Wataru and Tagoshi, Hideyuki

We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can be evaluated by solving the Teukolsky equation with a point like source term, which is computed from the stress-energy tensor of a test particle moving on generic bound geodesic orbits. In our previous papers, we computed the homogeneous solutions of the Teukolsky equation using a formalism developed by Mano, Suzuki and Takasugi and showed that we could compute gravitational waves efficiently and very accurately in the case of circular orbits on the equatorial plane. Here, we apply this method to eccentric inclined orbits. The geodesics around a Kerr black hole have three constants of motion: energy, angular momentum and the Carter constant. We compute the rates of change of the Carter constant as well as those of energy and angular momentum. This is the first time that the rate of change of the Carter constant has been evaluated accurately. We also treat the case of highly eccentric orbits with $latex e=0.9$. To confirm the accuracy of our codes, several tests are performed. We find that the accuracy is only limited by the truncation of $latex \ell$-, $latex k$- and $latex n$-modes, where $latex \ell$ is the index of the spin-weighted spheroidal harmonics, and $latex n$ and $latex k$ are the harmonics of the radial and polar motion, respectively. When we set the maximum of $latex \ell$ to 20, we obtain a relative accuracy of $latex 10^{-5}$ even in the highly eccentric case of $latex e=0.9$. The accuracy is better for lower eccentricity. Our numerical code is expected to be useful for computing templates of the extreme mass ratio inspirals, which is one of the main targets of the Laser Interferometer Space Antenna (LISA).

by Sopuerta, Carlos F. and Yunes, Nicolas
24 pages, 8 figures, Revtex 4

[abridged] Chern-Simons (CS) modified gravity is a 4D effective theory that descends both from string theory and loop quantum gravity, and that corrects the Einstein-Hilbert action by adding the product of a scalar field and the parity-violating, Pontryagin density. In this theory, the gravitational field of spinning black holes is described by a modified Kerr geometry whose multipole moments deviate from the Kerr ones only at the fourth multipole, l = 4. We investigate possible signatures of this theory in the gravitational wave emission produced in the inspiral of stellar compact objects into massive black holes, both for intermediate- and extreme-mass ratios. We use the semi-relativistic approximation, where the trajectories are geodesics of the massive black hole geometry and the gravitational waveforms are obtained from a multipolar decomposition of the radiative field. The main CS corrections to the waveforms arise from modifications to the geodesic trajectories, due to changes to the massive black hole geometry, and manifest themselves as an accumulating dephasing relative to the general relativistic case. We also explore the propagation and the stress-energy tensor of gravitational waves in this theory. We find that, although this tensor has the same form as in General Relativity, the energy and angular momentum balance laws are indeed modified through the stress-energy tensor of the CS scalar field. These balance laws could be used to describe the inspiral through adiabatic changes in the orbital parameters, which in turn would enhance the dephasing effect. Gravitational-wave observations of intermediate- or extreme-mass ratio inspirals with advanced ground detectors or with LISA could use such dephasing to test the dynamical theory to unprecedented levels.

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 Zhidenko, Alexander
PhD thesis for defence in May, 2009, 103 pages, PDFLaTex, English and Portuguese versions

Black holes have their proper oscillations, which are called the quasi-normal modes. The proper oscillations of astrophysical black holes can be observed in the nearest future with the help of gravitational wave detectors. Quasi-normal modes are also very important in the context of testing of the stability of black objects, the anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence and in higher dimensional theories, such as the brane-world scenarios and string theory.

This dissertation reviews a number of works, which provide a thorough study of the quasi-normal spectrum of a wide class of black holes in four and higher dimensions for fields of various spin and gravitational perturbations. We have studied numerically the dependance of the quasi-normal modes on a number of factors, such as the presence of the cosmological constant, the Gauss-Bonnet parameter or the aether in the space-time, the dependance of the spectrum on parameters of the black hole and fields under consideration. By the analysis of the quasi-normal spectrum, we have studied the stability of higher dimensional Reissner-Nordstrom-de Sitter black holes, Kaluza-Klein black holes with squashed horizons, Gauss-Bonnet black holes and black strings. Special attention is paid to the evolution of massive fields in the background of various black holes. We have considered their quasi-normal ringing and the late-time tails. In addition, we present two new numerical techniques: a generalisation of the Nollert improvement of the Frobenius method for higher dimensional problems and a qualitatively new method, which allows to calculate quasi-normal frequencies for black holes, which metrics are not known analytically.

by Palenzuela, Juan Carlos Degollado; Dario Nunez; Carlos
17 pages, 8 figures

The explicit form of perturbation equation for the $latex \Psi_4$ Weyl scalar, containing the matter source terms, is derived for general type D spacetimes. It is described in detail the particular case of the Schwarzschild spacetime using in-going penetrating coordinates. As a practical application, we focused on the emission of gravitational waves when a black hole is perturbed by a surrounding dust-like fluid matter. The symmetries of the spacetime and the simplicity of the matter source allow, by means of a spherical harmonic decomposition, to study the problem by means of a one dimensional numerical code.

by Schutz, Bernard F. and Centrella, Joan and Cutler, Curt and Hughes, Scott A.
Science White Paper submitted to the Astro2010 Decadal Survey

This is a whitepaper submitted to the 2010 Astronomy Decadal Review process, addressing the potential tests of gravity theory that could be made by observations of gravitational waves in the milliHertz frequency band by the proposed ESA-NASA gravitational wave observatory LISA. A key issue is that observations in this band of binary systems consisting of black holes offer very clean tests with high signal-to-noise ratios. Gravitational waves would probe nonlinear gravity and could reveal small corrections, such as extra long-range fields that arise in unified theories, deviations of the metric around massive black holes from the Kerr solution, massive gravitons, chiral effects, and effects of extra dimensions. The availability of strong signals from massive black hole binaries as well as complex signals from extreme mass-ratio binaries is unique to the milliHertz waveband and makes LISA a particularly sensitive probe of the validity of general relativity.

by Favata, Marc
4 pages, 3 figures

Some astrophysical sources of gravitational-waves can produce a “memory effect,” which causes a permanent displacement of the test masses in a freely-falling gravitational-wave detector. The Christodoulou memory is a particularly interesting nonlinear form of memory that arises from the gravitational-wave stress-energy tensor’s contribution to the distant gravitational-wave field. This nonlinear memory contributes a non-oscillatory component to the gravitational-wave signal at leading (Newtonian-quadrupole) order in the waveform amplitude. Previous computations of the memory and its detectability considered only the inspiral phase of binary black hole coalescence. Using an “effective-one-body” (EOB) approach calibrated to numerical relativity simulations, as well as a simple fully-analytic model, the Christodoulou memory is computed for the inspiral, merger, and ringdown. The memory will be very difficult to detect with ground-based interferometers, but is likely to be observable in supermassive black hole mergers with LISA out to a redshift of two. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to “gravitate.”