PhD Comprehensive Exam | Brayden Hull, Investigations of Nonlinear Fields in Gravitation

DWE 1515

Candidate

Brayden Hull | Applied Mathematics, University of Waterloo

Title

Investigations of Nonlinear Fields in Gravitation

Abstract

General Relativity is one of the most elegant theories in physics as demonstrated by its predictability and its numerous experimental verifications since Albert Einstein published it over 100 years ago. General Relativity however has a fatal flaw, it predicts its own demise. This demise is through the inevitable production of spacetime singularities, most famously at the centre of a black hole. This breakdown of spacetime is hoped to be remedied by a quantum theory of gravity. However, at this time no such theory is generally accepted. In the process of searching for a quantum theory of gravity, theorists have made modifications to the gravitational action that differ from the action of General Relativity. These modifications have been demonstrated through, but are not limited to, higher dimensions, nonlinear Riemann curvature tensor terms, scalar fields, and nonlinear combinations of the electromagnetic field tensor. It is believed modifications will be present in a quantum theory of gravity and that General Relativity is a low energy limit. The aim of this research is to investigate the solutions of the gravitational field equations that arise from a gravitational action which contains nonlinear field terms. I will study black hole thermodynamics, evaluate their phase structure, and compare this structure to black holes in General Relativity. I will also investigate cosmological solutions with these nonlinear fields and obtain constraints on the free parameters in the theory from observational data.