Instabilities in Higher-Dimensional Theories of Gravity
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A number of models of nature incorporate dimensions beyond our observed four. In this thesis we examine some examples and consequences of classical instabilities that emerge in the higher-dimensional theories of gravity which can describe their low energy phenomenology. <br /><br /> We first investigate a gravitational instability for black strings carrying momentum along an internal direction. We argue that this implies a new type of solution that is nonuniform along the extra dimension and find that there is a boost dependent critical dimension for which they are stable. Our analysis implies the existence of an analogous instability for the five-dimensional black ring. We construct a simple mode of the black ring to aid in applying these results and argue that such rings should exist in any number of space-time dimensions. <br /><br /> Next we consider a recently constructed class of nonsupersummetric solutions of type IIB supergravity which are everywhere smooth and have no horizon. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the endpoint of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's 'fuzzball' proposal. <br /><br /> Finally, we consider an interesting braneworld cosmology in the Randall-Sundrum scenario constructed using a bulk space-time which corresponds to a charged AdS black hole. In particular, these solutions appear to 'bounce', making a smooth transition from a contracting to an expanding phase. By considering the space-time geometry more carefully, we demonstrate that generically in these solutions the brane will encounter a singularity in the transition region.