[0803.4482] The transition from adiabatic inspiral to geodesic plunge for a compact object around a massive Kerr black hole: Generic orbits

Authors: Pranesh A. Sundararajan

Date: 31 Mar 2008

Abstract: The inspiral of a stellar mass compact object falling into a massive Kerr black hole can be broken into three different regimes: An adiabatic inspiral phase, where the inspiral timescale is much smaller than the orbital period; a late-time radial infall, which can be approximated as a plunging geodesic; and a regime where the body transitions from the inspiral to plunge. In earlier work, Ori and Thorne have outlined a method to compute the trajectory during this transition for a compact object in a circular, equatorial orbit. We generalize this technique to include inclination and eccentricity.

Mar 31, 2008

0803.4482 (/preprints)
2008-03-31, 20:09 

[0803.3804] Gravitational waves from pulsations of neutron stars described by realistic Equations of State

Authors: Sebastiano Bernuzzi, Alessandro Nagar

Date: 26 Mar 2008

Abstract: In this work we discuss the time-evolution of nonspherical perturbations of a nonrotating neutron star described by a realistic Equation of State (EOS). We analyze 10 different EOS for a large sample of neutron star models. Various kind of generic initial data are evolved and the corresponding gravitational wave signals are computed. We focus on the dynamical excitation of fluid and spacetime modes and extract the corresponding frequencies. We employ a constrained numerical algorithm based on standard finite differencing schemes which permits stable and long term evolutions. Our code provides accurate waveforms and allows to capture, via Fourier analysis of the energy spectra, the frequencies of the fluid modes with an accuracy comparable to that of frequency domain calculations. The results we present here are useful for provindig comparisons with simulations of nonlinear oscillations of (rotating) neutron star models as well as testbeds for 3D nonlinear codes.

Mar 26, 2008

0803.3804 (/preprints)
2008-03-26, 17:58 

[0803.3433] Perturbed Kerr Black Holes can probe deviations from General Relativity

Authors: Enrico Barausse, Thomas P. Sotiriou

Date: 24 Mar 2008

Abstract: Although the Kerr solution is common to many gravity theories, its perturbations are different in different theories. Hence, perturbed Kerr black holes can probe deviations from General Relativity.

Mar 24, 2008

0803.3433 (/preprints)
2008-03-24, 20:09 

[0803.3162] Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries

Authors: Thibault Damour, Alessandro Nagar, Mark Hannam, Sascha Husa, Bernd Brugmann

Date: 21 Mar 2008

Abstract: The Effective-One-Body (EOB) formalism contains several flexibility parameters, notably $a_5$, $\vp$ and $\a$. We show here how to jointly determine the values of these parameters by simultaneously best-fitting the EOB waveform to two, independent, numerical relativity (NR) simulations of inspiralling and/or coalescing binary black hole systems: published Caltech-Cornell {\it inspiral} data on one side and newly computed {\it coalescence} data on the other side. The resulting, essentially unique, ‘best-fit’ EOB waveform is then shown to exhibit excellent agreement with NR coalescence data for several mass ratios. The dephasing between EOB and published Caltech-Cornell inspiral data is found to be smaller than $\pm 2\times 10ˆ{-4}$ gravitational wave cycles over the entire span ($\sim 3000M$, corresponding to 30 cycles) of the inspiral simulation. The dephasings between EOB and the new coalescence data are found to be smaller than: (i) $\pm 4\times 10ˆ{-3}$ gravitational wave cycles over $730M$ (11 cycles), in the equal mass case, and (ii) $\pm 8\times 10ˆ{-3}$ gravitational wave cycles over about $900M$ (17 cycles) in the 2:1 mass-ratio case. These new results corroborate the aptitude of the EOB formalism to provide accurate representations of general relativistic waveforms, which areneeded by currently operating gravitational wave detectors.

Mar 24, 2008

0803.3162 (/preprints)
2008-03-24, 09:40 

[0803.1303] Explicit exact expression for the Thomas precession

Authors: Sergei A. Klioner

Date: 9 Mar 2008

Abstract: This work gives an explicit exact expression for the Thomas precession arising in the framework of Special Theory of Relativity as the spatial rotation resulting from two subsequence Lorentz boosts. The final result for the orthogonal matrix of Thomas precession is given by Eqs. (21)--(25). A trivial calculation leads to the compact formula (26) for the angle of rotation due to Thomas precession.
In the framework of Gaia the special-relativistic Thomas precession is an important step in the derivation of an aberrational formula with the Mansouri-Sexl parameters. The latter formula will be used to test the Local Lorentz Invariance with Gaia data as will be explained elsewhere.

Mar 17, 2008

0803.1303 (/preprints)
2008-03-17, 09:20 

[gr-qc/0612060] Gravitational waves from intermediate-mass-ratio inspirals for ground-based detectors

Authors: Duncan A. Brown, Jeandrew Brink, Hua Fang, Jonathan R. Gair, Chao Li, Geoffrey Lovelace, Ilya Mandel, Kip S. Thorne

Date: 11 Dec 2006

Abstract: We explore the prospects for Advanced LIGO to detect gravitational waves from neutron stars and stellar mass black holes spiraling into intermediate-mass ($M\sim 50 M_\odot$ to $350 M_\odot$) black holes. We estimate an event rate for such \emph{intermediate-mass-ratio inspirals} (IMRIs) of up to $\sim 10$--$30 \mathrm{yr}ˆ{-1}$. Our numerical simulations show that if the central body is not a black hole but its metric is stationary, axisymmetric, reflection symmetric and asymptotically flat then the waves will likely be tri-periodic, as for a black hole. We report generalizations of a theorem due to Ryan (1995) which suggest that the evolutions of the waves' three fundamental frequencies and of the complex amplitudes of their spectral components encode (in principle) a full map of the central body's metric, full details of the energy and angular momentum exchange between the central body and the orbit, and the time-evolving orbital elements. We estimate that Advanced LIGO can measure or constrain deviations of the central body from a Kerr black hole with modest but interesting accuracy.

Mar 13, 2008

0612060 (/preprints/gr-qc)
2008-03-13, 20:50 

[0803.1853] Accuracy of the Post-Newtonian Approximation: Optimal Asymptotic Expansion for Quasi-Circular, Extreme-Mass Ratio Inspirals

Authors: Nicolas Yunes, Emanuele Berti

Date: 13 Mar 2008

Abstract: We study the accuracy of the post-Newtonian (PN) approximation and its formal region of validity, by investigating its optimal asymptotic expansion for the quasi-circular, adiabatic inspiral of a point particle into a Schwarzschild black hole. By comparing the PN expansion of the energy flux to numerical calculations in the perturbative Teukolsky formalism, we show that (i) the inclusion of higher multipoles is necessary to establish the accuracy of high-order PN terms, and (ii) the region of validity of PN theory is largest at relative O(1/cˆ6) (3PN order). The latter result suggests that the series diverges beyond 3PN order, at least in the extreme mass-ratio limit, probably due to the appearance of logarithmic terms in the energy flux. The study presented here is a first formal attempt to determine the region of validity of the PN approximation using asymptotic analysis. Therefore, it should serve as a template to perform similar studies on other systems, such as comparable-mass quasi-circular inspirals computed by high-accuracy numerical relativistic simulations.

Mar 13, 2008

0803.1853 (/preprints)
2008-03-13, 20:49 

[0803.1820] Analysis of spin precession in binary black hole systems including quadrupole-monopole interaction

Authors: Etienne Racine

Date: 12 Mar 2008

Abstract: We analyze in detail the spin precession equations in binary black hole systems, when the tidal torque on a Kerr black hole is taken into account. We show that completing the precession equations with this term reveals the existence of a conserved quantity at 2PN order when restricting attention to orbits with negligible eccentricity and averaging over orbital motion. This quantity allows one to solve the (orbit-averaged) precession equations exactly in the case of equal masses and arbitrary spins, neglecting radiation reaction. For unequal masses, an exact solution does not exist in closed form, but we are still able to derive accurate approximate analytic solutions. We also show how to incorporate radiation reaction effects into our analytic solutions adiabatically, and compare the results to solutions obtained numerically. For various configurations of the binary, the relative difference in the accumulated orbital phase computed using our analytic solutions versus a full numerical solution vary from about 0.3% to 1.8% over the 80 - 140 orbital cycles accumulated while sweeping over the orbital frequency range 20 - 300 Hz. This typically corresponds to a discrepancy of order 5-6 radians. While this may not be accurate enough for implementation in LIGO template banks, we still believe that our new solutions are potentially quite useful for comparing numerical relativity simulations of spinning binary black hole systems with post-Newtonian theory. They can also be used to gain more understanding of precessional effects, with potential application to the gravitational recoil problem, and to provide semi-analytical templates for spinning, precessing binaries.

Mar 13, 2008

0803.1820 (/preprints)
2008-03-13, 09:09 

[0803.0862] xPerm: fast index canonicalization for tensor computer algebra

Authors: Jose M. Martin-Garcia

Date: 6 Mar 2008

Abstract: We present a very fast implementation of the Butler-Portugal algorithm for index canonicalization with respect to permutation symmetries. It is called xPerm, and has been written as a combination of a Mathematica package and a C subroutine. The latter performs the most demanding parts of the computations and can be linked from any other program or computer algebra system. We demonstrate with tests and timings the effectively polynomial performance of the Butler-Portugal algorithm with respect to the number of indices, though we also show a case in which it is exponential. Our implementation handles generic tensorial expressions with several dozen indices in hundredths of a second, or one hundred indices in a few seconds, clearly outperforming all other current canonicalizers. The code has been already under intensive testing for several years and has been essential in recent investigations in large-scale tensor computer algebra.

Mar 10, 2008

0803.0862 (/preprints)
2008-03-10, 09:31 

[0803.0915] Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling

Authors: Thibault Damour, Piotr Jaranowski, Gerhard Sch&#xe4;fer

Date: 6 Mar 2008

Abstract: Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the Effective One Body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the ‘effective’ Hamiltonian and the ‘real’ one, (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta, (iii) a Kerr-type effective metric (with Padé-resummed coefficients) which depends on the choice of some basic ‘effective spin vector’ $\bf{S}_{\rm eff}$, and which is deformed by comparable-mass effects, and (iv) an additional effective spin-orbit interaction term involving another spin vector $\bsigma$. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter $\hat{a}_{\rm LSO}\equiv c J_{\rm LSO}/\boldsymbol(G(H_{\rm LSO}/cˆ2)ˆ2\boldsymbol)$. We find that the inclusion of NLO spin-orbit terms has a significant ‘moderating’ effect on the dynamical characteristics of the circular orbits for large and parallel spins.

Mar 06, 2008

0803.0915 (/preprints)
2008-03-06, 22:15 

[0803.0786] On the independent points in the sky for the search of periodic gravitational wave

Authors: S.K. Sahay

Date: 6 Mar 2008

Abstract: We investigate the independent points in the sky require to search the periodic gravitational wave, assuming the noise power spectral density to be flat. We have made an analysis with different initial azimuth of the Earth for a week data set. The analysis shows significant difference in the independent points in the sky for the search. We numerically obtain an approximate relation to make trade-off between computational cost and sensitivities. We also discuss the feasibility of the coherent search in small frequency band in reference to advanced LIGO.

Mar 06, 2008

0803.0786 (/preprints)
2008-03-06, 22:15 

[0803.0003] Brightening of an Accretion Disk Due to Viscous Dissipation of Gravitational Waves During the Coalescence of Supermassive Black Holes

Authors: Bence Kocsis, Abraham Loeb (Harvard)

Date: 3 Mar 2008

Abstract: Mergers of supermassive black hole binaries release peak power of up to ~10ˆ57 erg/s in gravitational waves (GWs). As the GWs propagate through ambient gas, they induce shear and a small fraction of their power is dissipated through viscosity. The dissipated heat appears as electromagnetic (EM) radiation, providing a prompt EM counterpart to the GW signal. For thin accretion disks, the GW heating rate exceeds the accretion power at distances farther than 10ˆ3 Schwarzschild radii, independently of the accretion rate and viscosity coefficient.

Mar 04, 2008

0803.0003 (/preprints)
2008-03-04, 21:35 

[0803.0501] Possible Discovery of Nonlinear Tail and Quasinormal Modes in Black Hole Ringdown

Authors: Satoshi Okuzumi, Kunihito Ioka, Masa-aki Sakagami

Date: 4 Mar 2008

Abstract: We investigate the nonlinear evolution of black hole ringdown in the framework of higher-order metric perturbation theory. By solving the initial-value problem of a simplified nonlinear field model analytically as well as numerically, we find that (i) second-order quasinormal modes (QNMs) are indeed excited at frequencies different from those of first-order QNMs, as predicted recently. We also find serendipitously that (ii) late-time evolution is dominated by a new type of power-law tail. This ‘second-order power-law tail’ decays more slowly than any late-time tails known in the first-order (i.e., linear) perturbation theory, and is generated at the wavefront of the first-order perturbation by an essentially nonlinear mechanism. These nonlinear components should be particularly significant for binary black hole coalescences, and could open a new precision science in gravitational wave studies.

Mar 04, 2008

0803.0501 (/preprints)
2008-03-04, 21:34 

[0803.0390] Gravitational induction

Authors: Donato Bini, Christian Cherubini, Carmen Chicone, Bahram Mashhoon

Date: 4 Mar 2008

Abstract: We study the linear post-Newtonian approximation to general relativity known as gravitoelectromagnetism (GEM); in particular, we examine the similarities and differences between GEM and electrodynamics. Notwithstanding some significant differences between them, we find that a special nonstationary metric in GEM can be employed to show {\it explicitly} that it is possible to introduce gravitational induction within GEM in close analogy with Faraday's law of induction and Lenz's law in electrodynamics. Some of the physical implications of gravitational induction are briefly discussed.

Mar 04, 2008

0803.0390 (/preprints)
2008-03-04, 21:34 

[0803.0351] Extra-Large Remnant Recoil Velocities and Spins from Near-Extremal-Bowen-York-Spin Black-Hole Binaries

Authors: Sergio Dain, Carlos O. Lousto, Yosef Zlochower

Date: 4 Mar 2008

Abstract: We evolve equal-mass, equal-spin black-hole binaries with specific spins of a/mH 0.925, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counter-aligned and pointing in the orbital plane, which maximizes the recoil velocities of the merger remnant, as well as a configuration where the two spins point in the same direction as the orbital angular momentum, which maximizes the orbital hang-up effect and remnant spin. The coordinate radii of the individual apparent horizons in these cases are very small and the simulations require very high central resolutions (h~M/320). We find that these highly spinning holes reach a maximum recoil velocity of ~3300 km/s (the largest simulated so far) and, for the hangup configuration, a remnant spin of a/mH 0.922. These results are consistent with our previous predictions for the maximum recoil velocity of ~4000 km/s and remnant spin; the latter reinforcing the prediction that cosmic censorship is not violated by merging highly-spinning black-hole binaries. We also numerically solve the initial data for, and evolve, a single maximal-Bowen-York-spin black hole, and confirm that the 3-metric has an O(1/rˆ2) singularity at the puncture, rather than the usual O(1/rˆ4) singularity seen for non-maximal spins.

Mar 04, 2008

0803.0351 (/preprints)
2008-03-04, 21:33 

[0803.0317] Towards adiabatic waveforms for inspiral into Kerr black holes: II. Dynamical sources and generic orbits

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

Date: 3 Mar 2008

Abstract: This is the second in a series of papers whose aim is to generate ‘adiabatic’ gravitational waveforms from the inspiral of stellar-mass compact objects into massive black holes. In earlier work, we presented an accurate (2+1)D finite-difference time-domain code to solve the Teukolsky equation, which evolves curvature perturbations near rotating (Kerr) black holes. The key new ingredient there was a simple but accurate model of the singular source term based on a discrete representation of the Dirac-delta function and its derivatives. Our earlier work was intended as a proof of concept, using simple circular, equatorial geodesic orbits as a testbed. Such a source is effectively static, in that the smaller body remains at the same coordinate radius and orbital inclination over an orbit. (It of course moves through axial angle, but we separate that degree of freedom from the problem. Our numerical grid has only radial, polar, and time coordinates.) We now extend the time-domain code so that it can accommodate dynamic sources that move on a variety of physically interesting world lines. We validate the code with extensive comparison to frequency-domain waveforms for cases in which the source moves along generic (inclined and eccentric) bound geodesic orbits. We also demonstrate the ability of the time-domain code to accommodate sources moving on interesting non-geodesic worldlines. We do this by computing the waveform produced by a test mass following a ‘kludged’ inspiral trajectory, made of bound geodesic segments driven toward merger by an approximate radiation loss formula.

Mar 04, 2008

0803.0317 (/preprints)
2008-03-04, 12:36 

[0802.4320] Astrophysically Triggered Searches for Gravitational Waves: Status and Prospects

Authors: The LIGO Scientific Collaboration, Virgo Collaboration

Date: 29 Feb 2008

Abstract: In gravitational-wave detection, special emphasis is put onto searches that focus on cosmic events detected by other types of astrophysical observatories. The astrophysical triggers, e.g. from gamma-ray and X-ray satellites, optical telescopes and neutrino observatories, provide a trigger time for analyzing gravitational wave data coincident with the event. In certain cases the expected frequency range, source energetics, directional and progenitor information is also available. Beyond allowing the recognition of gravitational waveforms with amplitudes closer to the noise floor of the detector, these triggered searches should also lead to rich science results even before the onset of Advanced LIGO. In this paper we provide a broad review of LIGO's astrophysically triggered searches and the sources they target.

Mar 04, 2008

0802.4320 (/preprints)
2008-03-04, 12:35 

[0802.4427] Numerical Relativity meets Data Analysis: Spinning Binary Black Hole Case

Authors: Deirdre Shoemaker, Birjoo Vaishnav, Ian Hinder, Frank Herrmann

Date: 29 Feb 2008

Abstract: We present a study of the gravitational waveforms from a series of spinning, equal-mass black hole binaries focusing on the harmonic content of the waves and the contribution of the individual harmonics to the signal-to-noise ratio. The gravitational waves were produced from two series of evolutions with black holes of initial spins equal in magnitude and anti-aligned with each other. In one series the magnitude of the spin is varied; while in the second, the initial angle between the black-hole spins and the orbital angular momentum varies. We also conduct a preliminary investigation into using these waveforms as templates for detecting spinning binary black holes. Since these runs are relativity short, containing about two to three orbits, merger and ringdown, we limit our study to systems of total mass greater than 50 solar masses. This choice ensures that our waveforms are present in the ground-based detector band without needing addition gravitational wave cycles. We find that while the mode contribution to the signal-to-noise ratio varies with the initial angle, the total mass of the system caused greater variations in the match.

Mar 04, 2008

0802.4427 (/preprints)
2008-03-04, 12:35 

[0802.4169] String theory, gravity and experiment

Authors: Thibault Damour, Marc Lilley

Date: 28 Feb 2008

Abstract: The aim of these lectures is to give an introduction to several topics which lie at the intersection of string theory, gravity theory and gravity phenomenology. One successively reviews: (i) the "membrane" approach to the dissipative dynamics of classical black holes, (ii) the current experimental tests of gravity, and their theoretical interpretation, (iii) some aspects of the string-inspired phenomenology of the gravitational sector, and (iv) some possibilities for observing string-related signals in cosmology (including a discussion of gravitational wave signals from cosmic superstrings).

Mar 04, 2008

0802.4169 (/preprints)
2008-03-04, 12:34 

[0802.3411] Detecting Planets around Compact Binaries with Gravitational Wave Detectors in Space

Authors: Naoki Seto

Date: 22 Feb 2008

Abstract: I propose a method to detect planets around compact binaries that are strong sources of gravitational radiation. This approach is to measure gravitational-wave phase modulations induced by the planets, and its prospect is studied with a Fisher matrix analysis. I find that, using the Laser Interferometer Space Antenna (LISA), planets can be searched for around ~3000 Galactic double white dwarfs with detection limit ~4 M_J (M_J~ 2x10ˆ{30}g: the Jupiter mass). With its follow-on missions, planets with mass ~1 M_J might be detected around double neutron stars even at cosmological distances z~1. In this manner, gravitational wave observation has potential to make interesting contributions to extra-solar planetary science.

Mar 04, 2008

0802.3411 (/preprints)
2008-03-04, 12:33 

[0802.4047] Introductory lectures on the Effective One Body formalism

Authors: Thibault Damour

Date: 27 Feb 2008

Abstract: The Effective One Body (EOB) formalism is an analytical approach which aims at providing an accurate description of the motion and radiation of coalescing binary black holes. We present a brief review of the basic elements of this approach.

Mar 04, 2008

0802.4047 (/preprints)
2008-03-04, 12:33 

[0802.3210] Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes: Numerical Methods and Tests

Authors: Brian D. Farris, Tsz Ka Li, Yuk Tung Liu, Stuart L. Shapiro (UIUC)

Date: 21 Feb 2008

Abstract: Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized gas flowing in a strongly-curved, dynamical spacetime. Such systems include coalescing compact binaries containing neutron stars or white dwarfs, disks around merging black holes, core collapse supernovae, collapsars, and gamma-ray burst sources. To model these phenomena, all of which involve general relativity, radiation (photon and/or neutrino), and magnetohydrodynamics, we have developed a general relativistic code capable of evolving MHD fluids and radiation in dynamical spacetimes. Our code solves the coupled Einstein-Maxwell-MHD-Radiation system of equations both in axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the BSSN equations, and use a conservative, high-resolution shock-capturing scheme to evolve both the MHD and radiation moment equations. In this paper, we implement our scheme for optically thick gases and grey-body opacities. Our code gives accurate results in a suite of tests involving radiating shocks and nonlinear waves propagating in Minkowski spacetime. In addition, to test our code's ability to evolve the relativistic radiation-MHD equations in strong-field dynamical spacetimes, we study "thermal Oppenheimer-Snyder collapse" to a black hole, and find good agreement between analytic and numerical solutions.

Mar 04, 2008

0802.3210 (/preprints)
2008-03-04, 12:31