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Authors: Alex Harvey, Engelbert L. Schucking, Eugene J. Surowitz

Date: Wed, 31 Aug 2005

Abstract: Courses in introductory special and general relativity have increasingly become part of the curriculum for upper-level undergraduate physics majors and master's degree candidates. One of the topics rarely discussed is symmetry, particularly in the theory of general relativity. The principal tool for its study is the Killing vector. We provide an elementary introduction to the concept of a Killing vector field, its properties, and as an example of its utility apply these ideas to the rigorous determination of gravitational and cosmological redshifts.

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Authors: Réjean J. Dupuis, Graham Woan

Date: Tue, 23 Aug 2005

Abstract: We present a method of searching for, and parameterizing, signals from known radio pulsars in data from interferometric gravitational wave detectors. This method has been applied to data from the LIGO and GEO 600 detectors to set upper limits on the gravitational wave emission from several radio pulsars. Here we discuss the nature of the signal and the performance of the technique on simulated data. We show how to perform a coherent multiple detector analysis and give some insight in the covariance between the signal parameters.

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Authors: David B. Malament

Date: Thu, 18 Aug 2005

Abstract: This survey paper is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the "geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its "causal structure".

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Authors: S. Klimenko (1), S. Mohanty (2), M. Rakhmanov (1), G. Mitselmakher (1). ((1) University of Florida, Gainesville, FL. (2) University of Texas at Brownsville, TX.)

Date: Thu, 18 Aug 2005

Abstract: We propose a coherent method for the detection and reconstruction of gravitational wave signals for a network of interferometric detectors. The method is derived using the likelihood functional for unknown signal waveforms. In the standard approach, the global maximum of the likelihood over the space of waveforms is used as the detection statistic. We identify a problem with this approach. In the case of an aligned pair of detectors, the detection statistic depends on the cross-correlation between the detectors as expected, but this dependence dissappears even for infinitesimally small misalignments. We solve the problem by applying constraints on thelikelihood functional and obtain a new class of statistics. The resulting method can be applied to the data from a network consisting of any number of detectors with arbitrary detector orientations. The method allows us reconstruction of the source coordinates and the waveforms of two polarization components of a gravitational wave. We study the performance of the method with numerical simulation and find the reconstruction of the source coordinates to be more accurate than in the standard approach.

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Authors: Alessandra Buonanno, Yanbei Chen, Thibault Damour

Date: Tue, 16 Aug 2005

Abstract: We investigate the non-adiabatic dynamics of spinning black hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular momentum losses on quasi-circular orbits. We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the Effective One-Body approach. We focus on the influence of spin terms onto the dynamics and waveforms. We evaluate the energy and angular momentum released during the final stage of inspiral and plunge. For an equal-mass binary the energy released between 40Hz and the frequency beyond which our analytical treatment becomes unreliable is found to be, when using the more reliable Effective One-Body dynamics: 0.6% M for anti-aligned maximally spinning black holes, 5% M for aligned maximally spinning black hole, and 1.8% M for non-spinning configurations. In confirmation of previous results, we find that, for all binaries considered, the dimensionless rotation parameter J/Eˆ2 is always smaller than unity at the end of the inspiral, so that a Kerr black hole can form right after the inspiral phase. By matching a quasi-normal mode ringdown to the last reliable stages of the plunge, we construct complete waveforms approximately describing the gravitational wave signal emitted by the entire process of coalescence of precessing binaries of spinning black holes.

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Authors: Clovis Hopman, Tal Alexander (Weizmann)

Date: Mon, 15 Aug 2005

Abstract: We study the orbital parameters distribution of stars that are scattered into nearly radial orbits and then spiral into a massive black hole (MBH) due to dissipation, in particular by emission of gravitational waves (GW). This is important for GW detection, e.g. by the Laser Interferometer Space Antenna (LISA). Signal identification requires knowledge of the waveforms, which depend on the orbital parameters. We use analytical and Monte Carlo methods to analyze the interplay between GW dissipation and scattering in the presence of a mass sink during the transition from the initial scattering-dominated phase to the final dissipation-dominated phase of the inspiral. Our main results are (1) Stars typically enter the GW-emitting phase with high eccentricities. (2) The GW event rate per galaxy is a few per Gyr for typical central stellar cusps, almost independently of the relaxation time or the MBH mass. (3) For intermediate mass black holes (IBHs) of ~a thousand solar masses such as may exist in dense stellar clusters, the orbits are very eccentric and the inspiral is rapid, so the sources are very short-lived.

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Authors: Jonathan R Gair, Daniel J Kennefick, Shane L Larson

Date: Thu, 11 Aug 2005

Abstract: The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna (LISA). This paper calculates, using a semi-relativistic approximation, the total energy and angular momentum lost to gravitational radiation by compact bodies on very high eccentricity orbits passing close to a supermassive black hole; these quantities determine the characteristics of the orbital evolution necessary to estimate the capture rate. The semi-relativistic approximation improves upon treatments which use orbits at Newtonian order and quadrupolar radiation emission, and matches well onto accurate Teukolsky simulations for low eccentricity orbits. Formulae are presented for the semi-relativistic energy and angular momentum fluxes as a function of general orbital parameters.

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Authors: Linqing Wen, Bernard F Schutz (AEI, Germany)

Date: Wed, 10 Aug 2005

Abstract: A network of gravitational wave detectors is called redundant if, given the direction to a source, the strain induced by a gravitational wave in one or more of the detectors can be fully expressed in terms of the strain induced in others in the network. Because gravitational waves have only two polarizations, any network of three or more differently oriented interferometers with similar observing bands is redundant. For LISA, this ‘null’ output is known as the Sagnac mode, and its use in discriminating between detector noise and a cosmological gravitational wave background is well understood [1][2]. But the usefulness of the null veto for ground-based detector networks has been ignored until now. We show that it should make it possible to discriminate in a model-independent way between real gravitational waves and accidentally coincident non-Gaussian noise ‘events’ in redundant networks of two or more broadband detectors (e.g, three LIGO detectors and GEO). It has been shown that with three detectors, the null output can be used to locate the direction to the source, and then two other linear combinations of detector outputs give the optimal ‘coherent’ reconstruction of the two polarization components of the signal. We discuss briefly the implementation of such a detection strategy in realistic networks.

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Authors: Edward K. Porter

Date: Tue, 9 Aug 2005

Abstract: In this study we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test-particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ~0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q > 0. For q < 0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family. However, for parameter estimation, the P-approximant templates still outperforms the T-approximants.

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Authors: Edgar Everhart, Edward T. Pitkin

Ref: American Journal of Physics 51, 712 (1983)

Abstract: Universal variables offer a considerable improvement on classical methods of solving the two-body problem. The method has the same structure regardless of whether the orbit is an ellipse, parabola, or hyperbola. The near-parabolic orbit is handled with ease. Universal variables are particularly useful when starting with a position-velocity vector at time zero and finding this vector at any other time. This paper is tutorial, written in the belief that this method should be better known. A laboratory exercise is described which uses universal variables in plotting orbits in the solar system. The Appendix contains a concise derivation of the equations for universal variables.

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