Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2004.Includes bibliographical references (p. 77-78).An important subject in current gravity research concerns the evolution of compact binary systems in which both members spin, particularly in the extreme mass ratio limit. Previous research has suggested that the effect of spin in such systems may be particularly significant-possibly even chaotic-near the homoclinic set of orbits, which lie close to the separatrix dividing stable and unstable orbits. In this thesis we present a study of the spin-induced evolution of inclined, eccentric Kerr black hole orbits. The evolution of the orbital energy, angular momentum, and Carter constant for such orbits is driven by the local spin force on the orbiting body, which is inferred from the Papapetrou equations. We find that the variation of the constants which characterize the orbit (e.g., energy, angular momentum, and Carter constant) is complicated and occurs on orbital timescales, but is contained within well-defined bounds that expand smoothly as the spin on the orbiting body is increased. As a consequence, the total volume explored in the orbital phase space of a given orbit is finite. We also find that the phase space volume grows rapidly as one approaches the homoclinic set of orbits, but ceases to increase once the particle comes within a certain threshold distance of the separatrix.by Akash Pravin Kansagra.S.B
