Gauss-Bonnet Theories of Gravity in Four Dimensions

Abstract

In this thesis, we discuss Gauss-Bonnet theories of gravity, with a focus on the topic of 4D Einstein-Gauss-Bonnet gravity, which has been the subject of considerable interest over the past years. The thesis begins with a general introduction to gravitational physics, General Relativity, and its successes and shortcomings. We review Lovelock's theorem, and the subject of Gauss-Bonnet terms in the action for gravity. These areas are of fundamental importance for understanding modified theories of gravity, and inform our subsequent discussion of recent attempts to include the effects of a Gauss-Bonnet term in four spacetime dimensions by re-scaling the appropriate coupling parameter. We discuss the mathematical complexities involved in implementing this idea, and attempts at constructing well-defined, self-consistent theories that enact it. We then move on to consider the gravitational physics that results from these theories, in the context of black holes, cosmology, and weak-field gravity, showing that 4D Einstein-Gauss-Bonnet gravity exhibits a number of interesting phenomena in each of these areas. We follow up with the derivation of a generalized conformally coupled scalar field theory, which turns out to be intimately connected with the well-defined 4D Einstein Gauss-Bonnet gravity theories, and study its phenomenology. Adopting a more standard framework for Gauss-Bonnet theories in four dimensions, we also study the small mass limit of black holes and how it impacts on the self-consistency of these models. Finally, we study how spectral methods can be used to solve, with high accuracy, the systems of partial differential equations that result from the stationary and axisymmetric gravitational field equations in (generic) modified theories of gravity, obtaining with success spinning black holes in General Relativity, as a benchmark, and scalar-Gauss-Bonnet gravity. The estimated accuracy of the obtained solutions represent an improvement of several orders of magnitude with respect to other existing codes.