This thesis presents a study of several problems and issues in the nascent field of gravitational-wave astronomy. Multi-kilometer baseline interferometers are being built in the United States [the LIGO (Laser Interferometer Gravitational-wave Observatory) project] and similar projects are underway in Europe (the VIRGO and GE0600 projects) and Japan (the TAMA300 project). LIGO will begin operations very soon (the first science run is scheduled for 2002), and detectors in other countries will begin soon as well. We are thus about 5 years from using gravitational waves as a new window to probe astrophysical processes in the universe.
Chapters 2, 3, and 4 of this thesis study gravitational waves from coalescences of compact binaries. Chapters 2 and 3 are a detailed examination, in collaboration with Éanna É. Flanagan, of binary black hole (BBH) coalescences. The birth rate of BBH systems in the universe is highly uncertain, so it is not immediately apparent how relevant they are to gravitational-wave astronomy. If such systems do in fact exist, we find that they will be visible to extremely large distances, far greater than the distances to which binary neutron star systems, for example, will be visible. This heightened visibility may compensate for the possible dearth of such binaries, making them an extremely important and interesting source. We suggest ways in which numerical modeling of BBHs may aid gravitational-wave data analysis, and techniques that can be used in BBH event searches and waveform analysis. Chapter 4 analyzes the measurement of gravitational waves from the final merger of binary neutron star systems. Such waves depend on details of the composition of neutron stars, such as their equation of state, and may be driven by hydrodynamic and nuclear processes that occur in the final merger. Unfortunately, these waves are emitted at high frequencies where LIGO type detectors have poor sensitivity. Measuring such waves will require specialty "narrow-band" detectors. In this chapter, I present an algorithm for optimally configuring a network of multiple LIGO-type and narrow-band detectors to measure these merger waves. I find that improved theoretical modeling of the final merger will play an important role in designing such networks and in the analysis of their data. In Chapter 5, in collaborationwith Patrick R. Brady, I analyze the stability of binary neutron star systems as they coalesce. Some rather controversial numerical calculations have found that neutron stars in binary systems are rendered unstable by their companion, and may collapse into black holes long before their final merger. This would have a huge impact on the gravitational waves such systems emit. The claimed effect is first-order in a particular expansion. Motivated by this claim, Brady and I perform a first-order expansion of the fluid and field equations of general relativity, in the limit in which one star is much smaller than the other. We find that no such effect can exist. Finally, Chapter 6 is an analysis, in collaboration with Kip S. Thorne, of seismic gravity-gradient noise, a noise source that may be of concern to future detector designs. This noise source arises from fluctuations in the density of the earth near and below a LIGO-type interferometer's test masses. It is gravitational in origin, and thus cannot be shielded. By carefully studying the geological structures in the earth near the two LIGO sites, considering the propagation of elastodynamic waves in such structures, and computing the gravitational fluctuations such waves cause, we find seismic gravity-gradient noise is likely to become unavoidable at frequencies below roughly 5 Hertz. This has strong implications on plans to improve the low frequency sensitivity of the LIGO detectors.
