Electronic Thesis and Dissertation Repository


Doctor of Philosophy




Martin Houde and Sree Ram Valluri


Since its publication in 1915, Einstein's theory of general relativity has yielded significant results; they include: analytical solutions to the Einstein field equations; improved analysis of orbital dynamics; and the prediction of gravitational wave (GW) radiation. Gravitation is the weakest of the fundamental interactions; and theoretical models of GW generation and propagation show that its detection poses a significant technical challenge. Unlike the study of electromagnetic radiation, experiments within the laboratory are virtually impossible; so astronomical sources of GW, such as binary black hole systems, offer an alternative. But GW detection remains difficult. The matched filtering techniques used to discriminate a GW signal from background noise, require GW templates; thus a theoretical foreknowledge of binary black hole evolution is needed.

Extreme mass-ratio binary black hole systems may be modelled by a massive Kerr black hole (KBH) and a test-particle in an inclined elliptical orbit. The GW spectrum is determined by the latus rectum (l), eccentricity (e), and inclination (iota) of the orbit, which gradually change with loss of energy and angular momentum. The evolution of these orbital characteristics is described by equations widely available in the literature; so it is essential that corroborative techniques be found to assure accuracy. The last stable orbit (LSO) is an important end-point at which the zoom and whirl of the test-particle becomes pronounced; this also affects the GW spectrum.

An analytical and numerical study of the influence of KBH spin (S) on l and e of an equatorial LSO was performed first, followed by the derivation of a formula for the Carter constant (Q) of an inclined orbit in terms of S, l and e. This analysis drew attention to the abutment, a family of retrograde near-polar orbits, at which the consistency of evolution equations for Q with respect to those for l and e was tested. Further, the evolution of iota was also treated. To leading order in S, evolution equations for Q are consistent with those of l and e. The relationship between the evolution equation for iota with respect to l and e contains a second-order effect, which is yet to be fully characterised.