A study of solutions and perturbations of spherically symmetric spacetimes in fourth order gravity.

Doctoral Thesis


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University of Cape Town

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.

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Includes bibliographical references.