Heterotic Braneworld Gravity

Abstract

In the past decade, there has been considerable interest in braneworld scenarios where the universe lives on a brane in a higher-dimensional bulk and gravity is modified. The heterotic braneworld scenario of Lukas, Ovrut, Stelle and Waldram (LOSW) is derived from Horava-Witten M-theory, where six of the eleven dimensions have been compactified on a Calabi-Yau manifold. The solution consists of two parallel three-branes separated by the 11th dimension with a scalar field in the bulk. In this dissertation we review some of the alternative theories of gravity, including the Kaluza-Klein model as an early example of a theory featuring extra dimensions, and the more recent braneworld models, in particular the models proposed by Randall and Sundrum, based on which many braneworld techniques were developed. We use these techniques to study gravity in the LOSW model, and explore the possibilities for a black hole solution. Using perturbation theory, we find that the zero mode sector consists of the graviton and the radion which is coupled to the bulk scalar field, and there is a continuum of massive states. The brane gravity is scalar-tensor with a Brans-Dicke parameter of ω = 0.5. Then we show that although it is possible to have a black string between the two branes, it suffers from a Gregory-Laflamme instability. We also show that it is not possible to obtain spherically symmetric solutions, so we solve the coupled brane and bulk Einstein equations for an axisymmetric metric. We obtain a solution which asymptotes the LOSW vacuum and resembles the black string. The solution looks like the Schwarzshild solution at a large distance, but the interbrane distance is not constant and the string becomes infinite as it reaches the Schwarzshild radius.