Geodesic geometry of some static axisymmetric vacuum spacetimes

Harder, David M.

Geodesic geometry of some static axisymmetric vacuum spacetimes

dc.contributor.advisor	Kalnins, Ernie G.
dc.contributor.advisor	Craig, Ian J.D.
dc.contributor.author	Harder, David M.
dc.date.accessioned	2019-12-01T23:30:54Z
dc.date.available	2019-12-01T23:30:54Z
dc.date.issued	2003
dc.date.updated	2019-11-20T23:15:38Z
dc.description.abstract	Solutions of Laplace's equation in terms of bispherical and toroidal coordinates are used to derive new exact exterior (vacuum), general relativistic fields, of static axially symmetric spacetimes. For each new metric we calculate the first Geroch relativistic multipole moments. By selecting solutions that have even multipole moments, and thus a plane of equatorial symmetry, we numerically generate the timelike geodesics of test particles confined to these planes. Approximate solutions of these orbits are calculated, fro~ which the precession of the perihelion is compared to that of the numerical results and those predicted by a method of Fernández-Jambrina and Hoenselaers (2001). Similar calculations are done in the bispherical case for the precession rate of the line of nodes of a perturbed circular orbit. Geodesics of zero angular momentum are also presented for various spacetimes. In general, it is observed that the trajectories of test particles can experience periods of gravitational repulsion. Furthermore, the toroidal solutions show that the period of oscillation of a test particle along the axis of a ring like mass distribution can increase as the mass of the source is increased. We also consider the application of bicyclide coordinates. In doing so the computation of Lamé-Wangerin functions are required. New results for the eigenfunctions for the Lamé equation of order -1/2 are produced. Analytic and numerical results are compared. The multipole moments and timelike geodesics of this solution are also presented.
dc.format.mimetype	application/pdf
dc.identifier.citation	Harder, D. M. (2003). Geodesic geometry of some static axisymmetric vacuum spacetimes (Thesis, Doctor of Philosophy (PhD)). The University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/13228	en
dc.identifier.uri	https://hdl.handle.net/10289/13228
dc.language.iso	en
dc.publisher	The University of Waikato
dc.rights	All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
dc.title	Geodesic geometry of some static axisymmetric vacuum spacetimes
dc.type	Thesis
pubs.place-of-publication	Hamilton, New Zealand	en_NZ
thesis.degree.grantor	The University of Waikato
thesis.degree.level	Doctoral
thesis.degree.name	Doctor of Philosophy (PhD)