General relativistic dynamics of spinning particles

Abstract

Coalescing binary systems are supposed to be good sources for gravitational radiation. The data analysis of gravitational wave signals is very much involved with matched filtering procedures. Thus, a detailed theoretical understanding is an essential pillar of gravitational wave astronomy. This thesis is devoted to improve the theoretical description of binary systems consisting of spinning objects. It starts with a study of the dynamical properties of spinning test particles as described by the Mathisson-Papapetrou equations. Provided that the frequencies offer a straight link to observations the pairs of geometrically different timelike geodesics with the same radial and azimuthal frequencies is examined for spinning test particles moving in Schwarzschild-de Sitter spacetime. Then this thesis deals with a Hamiltonian formulation of spinning particles in general relativity. Due to the spin condition the derivation of a Hamiltonian involves the implementation of constraints. A Hamiltonian function linearised in the particle s spin that includes the constraints by means of Dirac brackets is analysed. Since the Hamiltonian offers a wide range of applications to dynamical systems, the significance of the approximation in the spin is investigated. In order to improve the Hamiltonian formulation and expand it to higher orders in the particle s spin an action approach is employed to impose the constraints at the level of the action. At the end applications to future work and implications on observations are discussed.