Explicit models for spherical static fluids in Einstein-Gauss-Bonnet gravity.

Master of Science in Mathematics. University of KwaZulu-Natal, Westville 2016.In this research, we explore modifications to the Einstein-Hilbert action by examining exact barotropic distributions in Einstein-Gauss-Bonnet gravity (EGB). We consider exact solutions of interior models in stars in five-dimensional EGB theory with spherical symmetry. We start by giving a brief introduction to the theory of general relativity and thereafter give a review of EGB gravity. From basic astrophysical modeling using the static five-dimensional metric, we obtain classical differential geometric quantities and thereafter produce the EGB field equations. These equations are a set of highly nonlinear partial differential equations and it is very difficult to solve exactly. By imposing a transformation proposed by Durgapal and Bannerji (1983), the field equations are written in equivalent form. Earlier EGB models are reviewed. New classes of exact solutions to the Einstein equations in five dimensions are found and their physical features are studied. In the EGB case we find two exact models with constant density. The first solution is the generalized Schwarzchild model. The second solution corresponds to a specific value of the Gauss-Bonnet constant