Near optimal solution to the inverse problem for gravitational-wave bursts

We develop a method for determining the source direction (θ,φ) and the two waveforms h+(t), h×(t) of a gravitational-wave burst using noisy data from three wideband gravitational-wave detectors running in coincidence. The scheme does not rely on any assumptions about the waveforms and in fact it works for gravitational-wave bursts of any kind. To improve the accuracy of the solution for (θ,φ), h+(t), h×(t), we construct a near optimal filter for the noisy data which is deduced from the data themselves. We implement the method numerically using simulated data for detectors that operate, with white Gaussian noise, in the frequency band of 500–2500 Hz. We show that for broadband signals centered around 1 kHz with a conventional signal-to-noise ratio of at least 10 in each detector we are able to locate the source within a solid angle of 1×10^-5 sr. If the signals and the detectors’ band were scaled downwards in frequency by a factor ι, at fixed signal-to-noise ratio, then the solid angle of the source’s error box would increase by a factor ι^2. The simulated data are assumed to be produced by three detectors: one on the east coast of the United States of America, one on the west coast of the United States of America, and the third in Germany or Western Australia. For conventional signal-to-noise ratios significantly lower than 10 the method still converges to the correct combination of the relative time delays but it is unable to distinguish between the two mirror-image directions defined by the relative time delays. The angular spread around these points increases as the signal-to-noise ratio decreases. For conventional signal-to-noise ratios near 1 the method loses its resolution completely

Stability of Spherically Symmetric, Charged Black Holes and Multipole Moments for Stationary Systems

This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.</p

LIGO: The Laser Interferometer Gravitational-Wave Observatory

The goal of the Laser Interferometer Gravitational-Wave Observatory (LIGO) Project is to detect and study astrophysical gravitational waves and use data from them for research in physics and astronomy. LIGO will support studies concerning the nature and nonlinear dynamics of gravity, the structures of black holes, and the equation of state of nuclear matter. It will also measure the masses, birth rates, collisions, and distributions of black holes and neutron stars in the universe and probe the cores of supernovae and the very early universe. The technology for LIGO has been developed during the past 20 years. Construction will begin in 1992, and under the present schedule, LIGO's gravitational-wave searches will begin in 1998