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A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity.
Includes abstract.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867613236115800067 |
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| access_status_str | Open Access |
| author | Nzioki, Anne Marie |
| author2 | Dunsby, Peter K S |
| author_browse | Dunsby, Peter K S Nzioki, Anne Marie |
| author_facet | Dunsby, Peter K S Nzioki, Anne Marie |
| author_sort | Nzioki, Anne Marie |
| collection | Thesis |
| description | Includes abstract. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/4916 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:56.154Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/4916 A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity. Nzioki, Anne Marie Dunsby, Peter K S Mathematics and Applied Mathematics 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. 2014-07-31T08:10:12Z 2014-07-31T08:10:12Z 2013 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/4916 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Nzioki, Anne Marie A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity. |
| thesis_degree_str | Doctoral |
| title | A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity. |
| title_full | A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity. |
| title_fullStr | A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity. |
| title_full_unstemmed | A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity. |
| title_short | A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity. |
| title_sort | study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/4916 |
| work_keys_str_mv | AT nziokiannemarie astudyofsolutionsandperturbationsofsphericallysymmetricspacetimesinfourthordergravity AT nziokiannemarie studyofsolutionsandperturbationsofsphericallysymmetricspacetimesinfourthordergravity |