Made available in DSpace on 2015-05-14T12:14:12Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1343904 bytes, checksum: e6a827a05ce6f44bfd65a1e4edd24434 (MD5) Previous issue date: 2013-12-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis we obtain the geometry associated with a cosmic string in two different models of modified gravity, namely: f(R) and Gauss-Bonnet theories. We Determined the solutions for static cosmic string and spinning cosmic string, with and without interior structure in f(R) and a static cosmic string in Gauss-Bonnet theory. For the static case, we solved the Dirac equation, and determined the fermionic current. We also found, in the context general theory of relativity, one solution with rotation corresponding to a rotation cloud of strings(Letelier spacetime), by using the method of Newman-Janis. / Nesta tese obtemos a geometria gerada por cordas cósmicas em dois modelos de gravitação modificada, a saber: Teorias f(R) e de Gauss-Bonnet. Determinamos soluções que correspondem ao espaço-tempo gerado pela corda cósmica estática e a corda cósmica com rotação, com e sem estrutura interna em f(R), e a corda cósmica estática na teoria de Gauss-Bonnet. Para as soluções estáticas, resolvemos a equação de Dirac, e determinamos a corrente ferminóica. Encontramos, também, no contexto da Teoria da Relatividade Geral, uma solução com rotação para a nuvem de cordas(Espaço-tempo de Letelier), usando o método de Newman-Janis.

In the review part of the thesis we summarize various modified theories of gravity, especially those that are characterized by additional curvature invariants in the Lagrangian density. Further, we review non-twisting geometries, especially their Kundt subclass. Finally, from the principle of least action we derive field equations for the case with the Lagrangian density corresponding to an arbitrary function of the curvature invariants. In the original part of the thesis we explicitly express particular components of the field equations for non-gyratonic Kundt geometry in generic quadratic gravity in arbitrary dimension. Then we discuss how this, in general fourth order, field equations restrict the Kundt metric in selected geome- trically privileged situations. We also analyse the special case of Gauss-Bonnet theory. 1