Warped Compactification on General Manifolds

Abstract

If extra dimensions exist, what effects from these dimensions manifest in our 4-dimensional spacetime? We will study these effects by performing dimensional reductions on Lagrangians. This process is called compactification. Compactification reveals a new spectrum of masses and a collection of fields called Kaluza-Klein Towers. In this thesis, we attain the spectra in closed form and consider a more general class of spacetimes that are "warped product manifolds." We will show that the Kaluza-Klein spectrum for the free warped scalar field is the same as if the full product space were a direct product manifold (un-warped). In this process, we will derive the warped scalar Laplacian. We will also present a proof showing that there are no warped solutions for a graviton with a zero cosmological constant. This project expands on previous work to derive Kaluza-Klein spectra on general manifolds that are direct product manifolds.