The influence of gravity upon topology changing transitions and warped flux compactifications

We investigate the dynamics of the geometric transitions associated to compactified spacetimes. By including the effects of gravity we are able to follow the evolution of collapsing cycles as they attempt to undergo a topology changing transition. We perform investigations where we add a perturbation to the momentum of a static solution and observe the consequences this has on the spacetime, looking for evidence of black hole formation or collapsing cycles which could lead to singular geometry. First we look into two possible four dimensional spacelike solutions to the Einstein equations called instantons. These both have a two-sphere at the origin, these are called bolt singularities. We introduce an initial perturbation to reduce the two-sphere to a point. Rather than achieving this singular geometry we find that either a horizon forms, shielding a curvature singularity, or the cycle re-expands after an initial contraction phase. For the case where a horizon forms we identify the final state with a known analytic black-hole solution. In seven dimensions we simulate the gravitational dynamics of the conifold geometries (resolved and deformed) involved in the description of certain compact spacetimes. As the cycles of the conifold collapse towards a singular geometry we inevitably find that a horizon develops, shielding the external spacetime. The structure of the black hole is examined and we find a candidate for the final state of the collapse. In ten dimensions we investigate the time evolution due to gravitational dynamics of a spacetime which is commonly used in brane-cosmology and string compactifications called the Klebanov-Strassler geometry. Here black holes are sometimes formed but more commonly the cycles are seen to re-expand after reaching a minimum value, showing the stability of the solution against perturbations which would change its size