In recent years, there has been an upsurge in interest in three-dimensional
theories of gravity. In particular, two theories of massive gravity in three dimensions
hold strong promise in the search for fully consistent theories of quantum
gravity, an understanding of which will shed light on the problems of quantum
gravity in four dimensions. One of these theories is the “old” third-order theory
of topologically massive gravity (TMG) and the other one is a “new” fourth-order
theory of massive gravity (NMG). Despite this increase in research activity, the
problem of finding and classifying solutions of TMG and NMG remains a wide
open area of research. In this thesis, we provide explicit new solutions of massive
gravity in three dimensions and suggest future directions of research. These solutions belong to the Kundt class of spacetimes. A systematic analysis of the Kundt
solutions with constant scalar polynomial curvature invariants provides a glimpse
of the structure of the spaces of solutions of the two theories of massive gravity.
We also find explicit solutions of topologically massive gravity whose scalar
polynomial curvature invariants are not all constant, and these are the first such
solutions. A number of properties of Kundt solutions of TMG and NMG, such
as an identification of solutions which lie at the intersection of the full nonlinear and linearized theories, are also derived. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/6535 |
| Date | 15 October 2009 |
| Creators | Chakhad, Mohamed |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Format | electronic |
| Rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. |
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