Geometry of black holes and braneworlds in higher dimensions

This tliesis first discusses braneworld models, we explain how the bulk geometry in codimension 2 scenarios restricts braneworld fields in a way inconsistent with observation. We then show how generalising Einstein's equations to include Gauss-Bonnet terms avoids this problem and as an example we successfully reproduce the Priedmann-Robertson-Walker cosmology familiar in Einstein gravity. The work on braneworlds concludes with a detailed perturbation analysis of a simple conical space-time in Gauss-Bonnet gravity, non-trivially we find the standard four-dimensional Lichnerowicz equation on the brane even though the calculation is performed in six dimensions. Next, motivated by the microscopic description of black hole thermodynamics, we discuss Gubser and Mitra's conjectured relationship between classical and thermodynamic stability including a review of numerical and theoretical evidence for it. We then give an argument using a recently discovered ansatz for non-uniform smeared p-brane solutions that the conjecture fails in the generality in which it is proposed. The thesis emphasises the underlying relationship between world volume field theory and bulk gravity from a geometrical point of view throughout.