We investigate spherically-symmetric gravitational collapse in the presence of a single "large" extra dimension through the use of analytical and numerical techniques. This has bearing on higher-dimensional ideas concerning hypothetical objects called "black strings," or black holes extending into an extra circular dimension, which dimension we hereinafter label zeta. These putative objects were first seriously considered as elements of string theory but have relevance in simpler, higher-dimensional generalization of Einstein's general relativity. We assume a universe topologically consisting of a two-dimensional Lorentzian manifold crossed with the sphere, crossed again with the circle. We model the formation of a uniform black string via two modes—the collapse of a massless scalar field, and of pure gravitational waves consisting of (gaussian) distortions in the extra dimension. We report on and discuss two aspects of the nonlinear dynamics, viz., that in five dimensions larger-amplitude fields appear to collapse more slowly than their lower amplitude cousins; and that pure gravitational field collapse exhibits signs of self-similarity at the threshold between black string formation and dispersal of the collapsing field.

In this project we review the method of using c-extremization and computing anomalies to obtain AdS/CFT theories. We start with a quick introduction to CFT's and AdS/CFT correspondence which gives us the tools to later understand the 2D N= (2,0) SCFT and its gravity duals in particular AdS_5xS^5 and AdS_7xS^4 compactified on Riemann surfaces.