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

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## Date

2016

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## Abstract

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.

## Description

Master of Science in Mathematics. University of KwaZulu-Natal, Westville 2016.

## Keywords

Theses - Mathematics and Computer Science Education.