Mathematics – Logic
Scientific paper
Jun 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phdt........19y&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF OREGON, 1987.Source: Dissertation Abstracts International, Volume: 48-07, Section: B, page: 2009.
Mathematics
Logic
Scientific paper
The purpose of this dissertation is to study the properties of specific particle-like and cosmological solutions of general relativity. In the first part, we study the solution for the NUT geodesics which will help us to understand the physical interpretation of the NUT parameter. It is shown that the properties of the NUT geodesics are similar to the properties of the trajectories of a charged particle in a potential created by a magnetic monopole. The properties of the NUT geodesics are summarized as follows: (1) the orbits of test particles lie on the surface of a cone; (2) the sum of the orbital angular momentum of the test particle vec{rm L} and the field angular momentum vec{ rm S} due to the NUT parameter is conserved; (3) the magnitude of orbital and field angular momenta are constant, i.e. L = |vec{ rm L}| and S = | vec{rm S}|; (4) the angular momentum of the field generated by the NUT parameter is along the radial direction of the test particle, and is independent of the distance between the NUT parameter and test particle; (5) the three space components of the NUT geodesics are spherically symmetric and the time component depends on the direction of the axial singularity. The second part of this dissertation is the study of an inhomogeneous generalization of the Bianchi I cosmological solution which contains gravitational waves. This model considers the interaction of the initial inhomogeneities with the evolution of the background geometry, electromagnetic radiation, gravity waves and matter. In this model the initial inhomogeneities evolve at late times into gravitational waves, which are propagating through a smooth Bianchi I background. As the wave evolves it interacts with the global shear and different forms of energy. Around the origin the propagation of the wave is governed by the shear, where as, at later times the influence of the shear decreases and the radiation density dominates the solution. At even later times, the properties of the gravity wave are governed by the matter equation of state. The study of this solution is useful because it allows us to investigate how inhomogeneities can evolve into gravitational waves, and how primordial gravity waves interact with the background.
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