Theses and Dissertations

Date of Award

12-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Sergey Grigorian

Second Advisor

Dr. Paul Bracken

Third Advisor

Dr. Elena Poletaeva

Abstract

The aim of this thesis is to outline the mathematical machinery of general relativity, quantum gravity, cosmology and an introduction to string theory under one body of work. We will flesh out tensor algebra and the formalism of differential geometry. After deriving the Einstein field equation, we will outline its traditional applications. We then linearize the field equation by a perturbation method and describe the mathematics of gravitational waves and their spherical harmonic analysis. We then transition into the derivation of the Schwarzschild metric and the Kruskal coordinate transformation, in order to set the stage for quantum gravity. This sets the background in order to segway into the principles of cosmology. We then introduce the formalism of quantum mechanics and derive the Hawking radiation formula of a non-spinning blackhole. We describe the phenomenology of quantum scattering, Regge theory and its mathematical underpinnings. This allows us to introduce string theory by studying infinite momentum boosts and strings in two dimensions.

Comments

Copyright 2018 Hassan Kesserwani. All Rights Reserved.

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