Physics in Higher-Dimensional Manifolds
In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We then turn our attention to the problem of embedding any given n-dimensional spacetime within an (n+1)-dimensional manifold, paying special attention to how any structure from the extra dimension modifies the standard n-dimensional Einstein equations. Using results derived from this investigation and the formalism derived for test particles and gyroscopes, we systematically introduce three specific higher-dimensional models and classify their properties; including the Space-Time-Matter and two types of braneworld models. The remainder of the thesis concentrates on specific higher-dimensional cosmological models drawn from the above mentioned scenarios; including an analysis of the embedding of Friedmann-Lemaitre-Robertson-Walker submanifolds in 5-dimensional Minkowski and topological Schwarzschild spaces, and an investigation of the dynamics of a d-brane that takes the form of a thin shell encircling a (d+2)-dimensional topological black hole in anti-deSitter space. The latter is derived from a finite-dimensional action principle, which allows us to consider the canonical quantization of the model and the solutions of the resulting Wheeler-DeWitt equation.
School:University of Waterloo
School Location:Canada - Ontario
Source Type:Master's Thesis
Keywords:physics astronomy general relativity extra dimensions brane world scenarios kaluza klein theory space time matter
Date of Publication:01/01/2003