Nonlinear Fields in Gravitation: Investigations in Black Hole and Cosmological Spacetimes

Abstract

This thesis is devoted to the study of non-linear effects in gravity, with a focus on black hole and cosmological spacetimes. We wish to study the phenomenological consequences that non-linearity can play on these particular spacetimes. These non-linear affects are primarily focused through higher curvature corrections, non-linear electrodynamics, and scaler fields. As we focus on black hole and cosmological space time we split this thesis into three parts, with Part I serving as a review of classical gravity, and alternative theories studied within.

Part II is dedicated to the discussion and study of black holes within these theories. We study various regimes with both single and multiple non-linear effects present. We study the thermodynamics of black holes in higher curvature and higher dimensional black holes, where higher curvature corrections serve as the source of non-linear effects. We show novel phase behaviour for a certain black hole class we refer to as exotic black holes. We show a further result of these exotic black holes is that they can posses negative mass in spacetimes which are pseudo-de Sitter spaces -- asymptotically possessing positive curvature, but not constant. We investigate lower dimensional black hole solutions in general relativity coupled to nonlinear electrodynamics, and show how they all follow similar solution structure. We also look at lower dimensional black holes non-minimally coupled to non-linear scalar fields with linear and non-linear electrodynamics. We show that all black hole solutions sourced via a radial electric field are characterized by the solution from the general relativity case.

Part III focuses on the study of cosmology. We look at cosmological constraints on the novel 4-dimensional Einstein-Gauss-Bonnet Gravity. This is done through construction of a complete set of equations of motion for 1st order scalar perturbations, and makes use of ACTpol cosmological data. We also look to determine whether this theory of gravity can resolve cosmological fine tuning problems such as the horizon and flatness problems. We then discuss constraints of quantum energy conditions on FLRW spacetimes in general relativity. How a variable equations of state parameter will be constrained, and its connection with the recent DESI results. We also look at how a bouncing universe through a non-minimally coupled non-linear massive scalar can also be constrained.