Detection in coincidence of gravitational wave bursts with a network of interferometric detectors (I): Geometric acceptance and timing

Detecting gravitational wave bursts (characterised by short durations and poorly modelled waveforms) requires to have coincidences between several interferometric detectors in order to reject non-stationary noise events. As the wave amplitude seen in a detector depends on its location with respect to the source direction and as the signal to noise ratio of these bursts are expected to be low, coincidences between antennas may not be so likely. This paper investigates this question from a statistical point of view by using a simple model of a network of detectors; it also estimates the timing precision of a detection in an interferometer which is an important issue for the reconstruction of the source location, based on time delays.Comment: low resolution figure 1 due to file size problem

The TIGA technique for detecting gravitational waves with a spherical antenna

We report the results of a theoretical and experimental study of a spherical gravitational wave antenna. We show that it is possible to understand the data from a spherical antenna with 6 radial resonant transducers attached to the surface in the truncated icosahedral arrangement. We find that the errors associated with small deviations from the ideal case are small compared to other sources of error, such as a finite signal-to-noise ratio. An in situ measurement technique is developed along with a general algorithm that describes a procedure for determining the direction of an external force acting on the antenna, including the force from a gravitational wave, using a combination of the transducer responses. The practicality of these techniques was verified on a room-temperature prototype antenna.Comment: 15 pages, 14 figures, submitted to Physical Review

Domain Wall Spacetimes: Instability of Cosmological Event and Cauchy Horizons

The stability of cosmological event and Cauchy horizons of spacetimes associated with plane symmetric domain walls are studied. It is found that both horizons are not stable against perturbations of null fluids and massless scalar fields; they are turned into curvature singularities. These singularities are light-like and strong in the sense that both the tidal forces and distortions acting on test particles become unbounded when theses singularities are approached.Comment: Latex, 3 figures not included in the text but available upon reques

Binary black hole spectroscopy

We study parameter estimation with post-Newtonian (PN) gravitational waveforms for the quasi-circular, adiabatic inspiral of spinning binary compact objects. The performance of amplitude-corrected waveforms is compared with that of the more commonly used restricted waveforms, in Advanced LIGO and EGO. With restricted waveforms, the properties of the source can only be extracted from the phasing. For amplitude-corrected waveforms, the spectrum encodes a wealth of additional information, which leads to dramatic improvements in parameter estimation. At distances of $\sim 100$ Mpc, the full PN waveforms allow for high-accuracy parameter extraction for total mass up to several hundred solar masses, while with the restricted ones the errors are steep functions of mass, and accurate parameter estimation is only possible for relatively light stellar mass binaries. At the low-mass end, the inclusion of amplitude corrections reduces the error on the time of coalescence by an order of magnitude in Advanced LIGO and a factor of 5 in EGO compared to the restricted waveforms; at higher masses these differences are much larger. The individual component masses, which are very poorly determined with restricted waveforms, become measurable with high accuracy if amplitude-corrected waveforms are used, with errors as low as a few percent in Advanced LIGO and a few tenths of a percent in EGO. The usual spin-orbit parameter $\beta$ is also poorly determined with restricted waveforms (except for low-mass systems in EGO), but the full waveforms give errors that are small compared to the largest possible value consistent with the Kerr bound. This suggests a way of finding out if one or both of the component objects violate this bound. We also briefly discuss the effect of amplitude corrections on parameter estimation in Initial LIGO.Comment: 28 pages, many figures. Final version accepted by CQG. More in-depth treatment of component mass errors and detectability of Kerr bound violations; improved presentatio

High-frequency corrections to the detector response and their effect on searches for gravitational waves

Searches for gravitational waves with km-scale laser interferometers often involve the long-wavelength approximation to describe the detector response. The prevailing assumption is that the corrections to the detector response due to its finite size are small and the errors due to the long-wavelength approximation are negligible. Recently, however, Baskaran and Grishchuk (2004 Class. Quantum Grav. 21 4041) found that in a simple Michelson interferometer such errors can be as large as 10 percent. For more accurate analysis, these authors proposed to use a linear-frequency correction to the long wavelength approximation. In this paper we revisit these calculations. We show that the linear-frequency correction is inadequate for certain locations in the sky and therefore accurate analysis requires taking into account the exact formula, commonly derived from the photon round-trip propagation time. Also, we extend the calculations to include the effect of Fabry-Perot resonators in the interferometer arms. Here we show that a simple approximation which combines the long-wavelength Michelson response with the single-pole approximation to the Fabry-Perot transfer function produces rather accurate results. In particular, the difference between the exact and the approximate formulae is at most 2-3 percent for those locations in the sky where the detector response is greater than half of its maximum value. We analyse the impact of such errors on detection sensitivity and parameter estimation in searches for periodic gravitational waves emitted by a known pulsar, and in searches for an isotropic stochastic gravitational-wave background. At frequencies up to 1 kHz, the effect of such errors is at most 1-2 percent. For higher frequencies, or if more accuracy is required, one should use the exact formula for the response.Comment: 13 pages, 6 figures, accepted by Classical and Quantum Gravity for GWDAW12 proceeding

Time-Independent Gravitational Fields

This article reviews, from a global point of view, rigorous results on time independent spacetimes. Throughout attention is confined to isolated bodies at rest or in uniform rotation in an otherwise empty universe. The discussion starts from first principles and is, as much as possible, self-contained.Comment: 47 pages, LaTeX, uses Springer cl2emult styl