General relativity has a small number of known, exact solutions which model
astronomically relevant systems. These models are highly idealized situations.
Either perturbation theory or numerical simulations are typically needed to
produce more realistic models. Numerical simulations are time-consuming and
suffer from a difficulty in interpreting the results. In addition, global
properties of numerical solutions are nearly impossible to uncover. On the
other hand, standard perturbation methods are very difficult to implement
beyond the second order, which means they barely scratch the surface of
non-linear phenomena which distinguishes general relativity from Newtonian gravity.
This work
develops a method of finding exact solutions, inspired by perturbation
theory,
which have energy-momentum tensor components that approximately satisfy
desired relationships. We find a spherical lump of matter
which has a density profile $\mu \propto r^{-2}$ in a Robertson-Walker
background; it looks like a galaxy in an expanding universe.
We also find a plane-symmetric perturbation of
a Bianchi type I metric with a density profile $\mu \propto z^{-2}$; it
models a jet impacting a sheet-like structure.
The former solution involves a wormhole while the latter involves a
two dimensional singularity. These are both non-linear structures which
perturbation theory can never produce.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/24331 |
| Date | 13 April 2010 |
| Creators | Wilson, Brian James |
| Contributors | Dyer, Charles C. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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