Topics in gravitational-wave physics

Abstract

Together with ongoing experimental efforts to detect gravitational waves, several fronts of theoretical research are presently being pursued, including second-generation detector design, data analysis, and numerical-relativity simulations of sources. This thesis presents a study in each of these topics: i) The noise in the most sensitive frequency bands in second-generation ground-based gravitational-wave interferometers is dominated by the thermal noise of the test masses. One way to reduce test-mass thermal noise is to modify shape of the laser beam so that it better averages over the thermal fluctuations. When edge effects are neglected, the test-mass thermal noise is related to the beam shape by simple scaling laws. This thesis presents a rigorous derivation of these laws, along with estimates of the errors made by neglecting edge effects. ii) An important class of gravitational-wave sources for space-based gravitational-wave interferometers is extreme-mass-ratio inspirals (EMRIs). These are binaries in which an object of a few solar masses spirals into a (typically million-solar-mass) supermassive black hole (or, if any exist, other type of massive body). Ryan (1995) proved that, under certain simplifying assumptions, the spacetime geometry is redundantly encoded in EMRI waves. One of Ryan's assumptions was negligible tidal coupling. After first finding that only the time-varying part of the induced tide is unambiguously defined when the central body is a black hole, this thesis extends Ryan's theorem by showing that both the spacetime geometry and details of the tidal coupling are encoded in EMRI waves. iii) Merging black holes with comparable masses are important sources of gravitational waves for ground-based detectors. The gravitational waves near the time of merger can only be predicted by numerically solving the Einstein equations. Initial data in numerical simulations must contain the desired physical content but also satisfy the Einstein constraint equations. But conventional binary-black-hole initial data has physical flaws: a nonzero orbital eccentricity and an initial, unphysical pulse of spurious gravitational radiation. Using the Caltech-Cornell pseudospectral code, this thesis develops and implements methods to reduce both of these effects.