by Grossman, Rebecca and Levin, Janna and Perez-Giz, Gabe
30 pages, 7 figures. Submitted to Phys. Rev. D

Motivated by the prohibitive computational cost of producing adiabatic extreme mass ratio inspirals, we explain how a judicious use of resonant orbits can dramatically expedite both that calculation and the generation of snapshot gravitational waves from geodesic sources. In the course of our argument, we clarify the resolution of a lingering debate on the appropriate adiabatic averaging prescription in favor of torus averaging over time averaging.

by Koekoek, G. and van Holten, J. W.

The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and Zerilli-Moncrief equations, which describe the propagation of gravitational waves emitted by a compact massive object moving in the Schwarzschild background space-time. The wave equations are solved numerically to provide the asymptotic form of the wave at large distances for a series of non-circular bound orbits with periastron distances up to the ISCO radius, and the power emitted in gravitational waves by the extreme-mass ratio binary system is computed. The results compare well with those of purely numerical approaches.

by Harada, Tomohiro and Kimura, Masashi
21 pages, 3 figures, submitted to PRD

We obtain an explicit expression for the center-of-mass (CM) energy of two colliding general geodesic massive and massless particles at any spacetime point around a Kerr black hole. Applying this, we show that the CM energy can be arbitrarily high only in the limit to the horizon and then derive a formula for the CM energy of two general geodesic particles colliding near the horizon in terms of the conserved quantities of each particle and the polar angle. We present the necessary and sufficient condition for the CM energy to be arbitrarily high in terms of the conserved quantities of each particle. To have an arbitrarily high CM energy, the angular momentum of either of the two particles must be fine-tuned to the critical value $latex L_{i}=\Omega_{H}^{-1}E_{i}$, where $latex \Omega_{H}$ is the angular velocity of the horizon and $latex E_{i}$ and $latex L_{i}$ are the energy and angular momentum of particle $latex i$ ($latex =1,2$), respectively. We show that, in the direct collision scenario, the collision with an arbitrarily high CM energy can occur near the horizon of maximally rotating black holes not only at the equator but also on a belt centered at the equator. If the critical particle is massless, this belt lies between latitudes $latex \pm acos(\sqrt{3}-1)\simeq \pm 42.94^{\circ}$. If the critical particle is massive, the highest absolute value of the latitude depends on the specific energy of the critical particle but rises up to the same value as the specific energy is increased to infinity. This is also true in the scenario through the collision of a last stable orbit particle.

by Barack, Leor and Sago, Norichika
29 pages, 4 eps figures

We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle’s mass $latex \mu$ is much smaller than the black hole mass $latex M$, and explore post-geodesic corrections of $latex O(\mu/M)$. Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the $latex O(\mu/M)$ conservative correction to the periastron advance of the orbit, as a function of the (gauge dependent) semi-latus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler’s circular-orbit “red shift” invariant. We compute the $latex O(\mu/M)$ conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly-gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations.

by Canizares, Priscilla and Sopuerta, Carlos F.
IOP LaTeX style. 11 pages, 4 pages. Contribution to the NRDA/CAPRA 2010 Conference

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

by Mitsou, Ermis
15 pages, 7 figures

The computation of the gravitational radiation emitted by a particle falling into a Schwarzschild black hole is a classic problem studied already in the 1970s. Here we present a detailed numerical analysis of the case of radial infall starting at infinity with no initial velocity. We compute the radiated waveforms, spectra and energies for multipoles up to l = 6, improving significantly on the numerical accuracy of existing results. This is done by integrating the Zerilli equation in the frequency domain using the Green’s function method. The resulting wave exhibits a “ring-down” phase whose dominant contribution is a superposition of the quasi-normal modes of the black hole. The numerical accuracy allows us to recover the frequencies of these modes through a fit of that part of the wave. Comparing with direct computations of the quasi-normal modes we reach a \sim 10^{-4} to \sim 10^{-2} accuracy for the first two overtones of each multipole. Our numerical accuracy also allows us to display the power-law tail that the wave develops after the ring-down has been exponentially cut-off. The amplitude of this contribution is \sim 10^2 to \sim 10^3 times smaller than the typical scale of the wave.

by Antonucci, F and Armano, M and Audley, H and Auger, G and Benedetti, M and Binetruy, P and Boatella, C and Bogenstahl, J and Bortoluzzi, D and Bosetti, P and Brandt, N and Caleno, M and Cavalleri, A and Cesa, M and Chmeissani, M and Ciani, G and Conchillo, A and Congedo, G and Cristofolini, I and Cruise, M and Danzmann, K and De Marchi, F and Diaz-Aguilo, M and Diepholz, I and Dixon, G and Dolesi, R and Dunbar, N and Fauste, J and Ferraioli, L and Fertin, D and Fichter, W and Fitzsimons, E and Freschi, M and Marin, A García and Marirrodriga, C García and Gerndt, R and Gesa, L and Giardini, D and Gibert, F and Grimani, C and Grynagier, A and Guillaume, B and Guzmán, F and Harrison, I and Heinzel, G and Hewitson, M and Hollington, D and Hough, J and Hoyland, D and Hueller, M and Huesler, J and Jeannin, O and Jennrich, O and Jetzer, P and Johlander, B and Killow, C and Llamas, X and Lloro, I and Lobo, A and Maarschalkerweerd, R and Madden, S and Mance, D and Mateos, I and McNamara, P W and Mendestì, J and Mitchell, E and Monsky, A and Nicolini, D and Nicolodi, D and Nofrarias, M and Pedersen, F and Perreur-Lloyd, M and Perreca, A and Plagnol, E and Prat, P and Racca, G D and Rais, B and Ramos-Castro, J and Reiche, J and Perez, J A Romera and Robertson, D and Rozemeijer, H and Sanjuan, J and Schleicher, A and Schulte, M and Shaul, D and Stagnaro, L and Strandmoe, S and Steier, F and Sumner, T J and Taylor, A and Texier, D and Trenkel, C and Tombolato, D and Vitale, S and Wanner, G and Ward, H and Waschke, S and Wass, P and Weber, W J and Zweifel, P
Proceedings of the 8th LISA Symposium. Submitted to Classical and Quantum Gravity

This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware and flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor two of the LISA requirement at 1 mHz and within a factor 10 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement, that will guarantee the LISA performance.

by Gair, Jonathan R. and Flanagan, Eanna E. and Drasco, Steve and Hinderer, Tanja and Babak, Stanislav
27 pages, 2 figures, submitted to Phys. Rev. D

We present two methods for integrating forced geodesic equations in the Kerr spacetime, which can accommodate arbitrary forces. As a test case, we compute inspirals under a simple drag force, mimicking the presence of gas. We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitational-radiation-driven inspirals, and similar to what is observed in hydrodynamic simulations of gaseous binaries. We provide an analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If observed, an increasing eccentricity would provide clear evidence that the inspiral was occurring in a non-vacuum environment. Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In one method the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In the second method, the phase constants of the geodesic motion are evolved separately and the force is expressed in terms of its Boyer-Lindquist components. This second approach is a generalization of earlier work by Pound and Poisson for planar forces in a Schwarzschild background.

by Favata, Marc
17 pages, 2 figures, 1 table

The innermost stable circular orbit (ISCO) delimits the transition from circular orbits to those that plunge into a black hole. In the test-mass limit, well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes. In the finite-mass case, there are a large variety of ways to define an ISCO in a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO condition of Blanchet & Iyer (2003) to the case of spinning (non-precessing) binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass limit, and (2) it accurately approximates the recently-calculated shift in the Schwarzschild ISCO frequency due to the conservative-piece of the gravitational self-force [Barack & Sago (2009)]. The generalization of this ISCO condition to spinning binaries has the property that it also exactly reproduces the Kerr ISCO in the test-mass limit (up to the order at which PN spin corrections are currently known). The shift in the ISCO due to the spin of the test-particle is also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly reproduces the ISCO shift predicted by the Papapetrou equations for a fully-relativistic spinning particle. It is surprising that an analysis of the stability of the standard PN equations of motion is able (without any form of “resummation”) to accurately describe strong-field effects of the Kerr spacetime. The ISCO frequency shift due to the conservative self-force in Kerr is also calculated from this new ISCO condition, as well as from the effective-one-body Hamiltonian of Barausse & Buonanno (2010). These results serve as a useful point-of-comparison for future gravitational self-force calculations in the Kerr spacetime.

by Yunes, Nicolas and Miller, M. Coleman and Thornburg, Jonathan
9 pages, 3 figures, submitted to Phys. Rev. D

Extreme mass ratio inspirals, in which a stellar-mass object merges with a supermassive black hole, are prime sources for space-based gravitational wave detectors because they will facilitate tests of strong gravity and probe the spacetime around rotating compact objects. In the last few years of such inspirals, the total phase is in the millions of radians and details of the waveforms are sensitive to small perturbations. We show that one potentially detectable perturbation is the presence of a second supermassive black hole within a few tenths of a parsec. The acceleration produced by the perturber on the extreme mass-ratio system produces a steady drift that causes the waveform to deviate systematically from that of an isolated system. If the perturber is a few tenths of a parsec from the extreme-mass ratio system (plausible in as many as a few percent of cases) higher derivatives of motion might also be detectable. In that case, the mass and distance of the perturber can be derived independently, which would allow a new probe of merger dynamics.

by Canizares, Priscilla and Sopuerta, Carlos F.
6 pages, 7 figures, submitted to proceedings of the 8th International LISA Symposium, Stanford, June 28 – July 2, 2010

The gravitational-wave signals emitted by Extreme-Mass-Ratio Inspirals will be hidden in the instrumental LISA noise and the foreground noise produced by galactic binaries in the LISA band. Then, we need accurate gravitational-wave templates to extract these signals from the noise and obtain the relevant physical parameters. This means that in the modeling of these systems we have to take into account how the orbit of the stellar-mass compact object is modified by the action of its own gravitational field. This effect can be described as the action of a local force, the self-force. We present a time-domain technique to compute the self-force for geodesic eccentric orbits around a non-rotating massive black hole. To illustrate the method we have applied it to a testbed model consisting of scalar charged particle orbiting a non-dynamical black hole. A key feature of our method is that it does not introduce a small scale associated with the stellar-mass compact object. This is achieved by using a multidomain framework where the particle is located at the interface between two subdomains. In this way, we just have to evolve homogeneous wave-like equations with smooth solutions that have to be communicated across the subdomain boundaries using appropriate junction conditions. The numerical technique that we use to implement this scheme is the pseudospectral collocation method. We show the suitability of this technique for the modeling of Extreme-Mass-Ratio Inspirals and show that it can provide accurate results for the self-force.

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 Cerdonio, M. and De Marchi, F. and De Pietri, R. and Jetzer, P. and Marzari, F. and Mazzolo, G. and Ortolan, A. and Sereno, M.
15 pages, 5 figures

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 yr^-1 and a series of periodic perturbations with frequencies equal to integer harmonics of the synodic month (9.92 10^-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 10^-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.

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 Barack, Leor and Sago, Norichika
42 pages

We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a time-domain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxes of energy and angular momentum, which we extract independently from the wave-zone numerical solutions. The conservative piece of the self force does not affect the time-averaged rate of energy and angular-momentum loss, but it influences the evolution of the orbital phases; this piece is calculated here for the first time in eccentric strong-field orbits. As a first concrete application of our code we recently reported the value of the shift in the location and frequency of the innermost stable circular orbit due to the conservative self-force [Phys. Rev. Lett.\ {\bf 102}, 191101 (2009)]. Here we provide full details of this analysis, and discuss future applications.

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

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

by 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 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 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.