Includes abstract. / Includes bibliographical references. / In this thesis we use the 1+1+2 covariant approach to General Relativity to study exact solutions and perturbations of rotationally symmetric spacetimes in f(R) gravity, one of the most widely studied classes of fourth order gravity. We begin by introducing f(R) theories of gravity and present the general equations for these theories. We investigate the problem of matching different regions of spacetime, shedding light on the problem of constructing realistic inhomogeneous cosmologies in the context of f(R) gravity. We also study strong lensing in these fourth order theories of gravity derive the lens mass and magnification for the gravitational lens system. We provide an extensive review of both the 1+3 and 1+1+2 covariant approaches to f(R) theories of gravity and give the full system of evolution, propagation and constraint equations of LRS spacetimes. We then determine the conditions for the existence of spherically symmetric vacuum solutions of these fourth order field equations and prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity and the necessary conditions required for the existence of Schwarzschild solution in these theories.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/4916 |
| Date | January 2013 |
| Creators | Nzioki, Anne Marie |
| Contributors | Dunsby, Peter K S |
| Publisher | University of Cape Town, Faculty of Science, Department of Mathematics and Applied Mathematics |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Doctoral Thesis, Doctoral, PhD |
| Format | application/pdf |
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