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The foundations are laid for the numerical computation of the actual worldline for a particle orbiting a black hole and emitting gravitational waves. The essential practicalities of this computation are here illustrated for a scalar particle of infinitesimal size and small but finite scalar charge. This particle deviates from a geodesic because it interacts with its own retarded field ψ ret . A recently introduced [1] Green's function G S precisely determines the singular part, ψ S , of the retarded field. This part exerts no force on the particle. The remainder of the field ψ R = ψ ret − ψ S is a vacuum solution of the field equation and is entirely responsible for the self-force. A particular, locally inertial coordinate system is used to determine an expansion of ψ S in the vicinity of the particle. For a particle in a circular orbit in the Schwarzschild geometry, the mode-sum decomposition of the difference between ψ ret and the dominant terms in the expansion of ψ S provide a mode-sum decomposition of an approximation for ψ R from which the self-force is obtained. When more terms are included in the expansion, the approximation for ψ R is increasingly differentiable, and the mode-sum for the self-force converges more rapidly.

We carry out two searches for periodic gravitational waves using the most sensitive few hours of data from the second LIGO science run. Both searches exploit fully coherent matched filtering and cover wide areas of parameter space, an innovation over previous analyses which requires considerable algorithm development and computational power. The first search is targeted at isolated, previously unknown neutron stars, covers the entire sky in the frequency band 160 -728.8 Hz, and assumes a frequency derivative of less than 4 10 ÿ10 Hz=s. The second search targets the accreting neutron star in the lowmass x-ray binary Scorpius X-1 and covers the frequency bands 464-484 Hz and 604-624 Hz as well as the two relevant binary orbit parameters. Because of the high computational cost of these searches we limit the analyses to the most sensitive 10 hours and 6 hours of data, respectively. Given the limited sensitivity and duration of the analyzed data set, we do not attempt deep follow-up studies. Rather we concentrate on demonstrating the data analysis method on a real data set and present our results as upper limits over large volumes of the parameter space. In order to achieve this, we look for coincidences in parameter space between the Livingston and Hanford 4-km interferometers. For isolated neutron stars our 95% confidence level upper limits on the gravitational wave strain amplitude range from 6:6 10 ÿ23 to 1 10 ÿ21 across the frequency band; for Scorpius X-1 they range from 1:7 10 ÿ22 to 1:3 10 ÿ21 across the two 20-Hz frequency bands. The upper limits presented in this paper are the first broadband wide parameter space upper limits on periodic gravitational waves from coherent search techniques. The methods developed here lay the foundations for upcoming hierarchical searches of more sensitive data which may detect astrophysical signals.

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The Laser Interferometer Gravitational-Wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new Bayesian 90% upper limit is GW ; H 0 / 72 km s À1 Mpc À1 À Á Â Ã 2 < 6:5 ; 10 À5 . This is currently the most sensitive result in the frequency range 51Y150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss the complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.

For a particle of mass µ and scalar charge q, we compute the effects of the scalar field self-force upon circular orbits, upon slightly eccentric orbits and upon the innermost stable circular orbit of a Schwarzschild black hole of mass m. For circular orbits the self force is outward and causes the angular frequency at a given radius to decrease. For slightly eccentric orbits the self force decreases the rate of the precession of the orbit. The effect of the self force moves the radius of the innermost stable circular orbit inward by 0.122701 × q 2 /µ, and it increases the angular frequency of the ISCO by the fraction 0.0291657 × q 2 /µm.

We report on a search for gravitational waves from the coalescence of compact binaries during the third and fourth LIGO science runs. The search focused on gravitational waves generated during the inspiral phase of the binary evolution. In our analysis, we considered three categories of compact binary systems, ordered by mass: (i) primordial black hole binaries with masses in the range 0.35M center dot m(1), m(2) 1.0M center dot, (ii) binary neutron stars with masses in the range 1.0M center dot m(1), m(2) 3.0M center dot, and (iii) binary black holes with masses in the range 3.0M center dot m(1), m(2) m(max) with the additional constraint m(1) + m(2) m(max), where m(max) was set to 40.0M center dot and 80.0M center dot in the third and fourth science runs, respectively. Although the detectors could probe to distances as far as tens of Mpc, no gravitational-wave signals were identified in the 1364 hours of data we analyzed. Assuming a binary population with a Gaussian distribution around 0.75 - 0.75M center dot, 1.4 - 1.4M center dot, and 5.0 - 5.0M center dot, we derived 90%- confidence upper limit rates of 4.9 yr(-1)L(10)(-1) for primordial black hole binaries, 1.2 yr(-1)L(10)(-1) for binary neutron stars, and 0: 5 yr(-1)L(10)(-1) for stellar mass binary black holes, where L-10 is 10(10) times the blue-light luminosity of the Sun

The fourth science run of the LIGO and GEO 600 gravitational-wave detectors, carried out in early 2005, collected data with significantly lower noise than previous science runs. We report on a search for short-duration gravitationalwave bursts with arbitrary waveform in the 64-1600 Hz frequency range appearing in all three LIGO interferometers. Signal consistency tests, data quality cuts and auxiliary-channel vetoes are applied to reduce the rate of spurious triggers. No gravitational-wave signals are detected in 15.5 days of live observation time; we set a frequentist upper limit of 0.15 day −1 (at 90% confidence level) on the rate of bursts with large enough amplitudes to be detected reliably. The amplitude sensitivity of the search, characterized using Monte Carlo simulations, is several times better than that of previous searches. We also provide rough estimates of the distances at which representative supernova and binary black hole merger signals could be detected with 50% efficiency by this analysis.PACS numbers: 04.80. Nn, 95.85.Sz