Title:

The nuts and bolts of entropy

The first topic considers the boundary terms in a Hamiltonian approach to general relativity. We show that if a timelike boundary of a spacetime is not orthogonal to the constant time hypersurfaces, then an additional 'tilting' term must be included in the Hamiltonian. The second topic considers the actions and thermodynamics of spacetimes with 'nut charge'. We provide a consistent framework for calculating the action of these spacetimes by requiring a background subtraction based on a metric that satisfies the same asymptotic conditions. Using this formalism we then calculate the action for metrics with a U(1) isometry, using both dimensional reduction and a Hamiltonian decomposition. In the former case we obtain a formula in terms of quantities defined on the fixed point set of the isometry, including explicit nut charge contributions. In the latter case the action depends on a surface integral at infinity, as well as on surface integrals and areas of the two dimensional obstructions to foliations based on the isometry  the wellknown 'bolts' of the isometry and the novel 'Misner strings' that arise from the nut charge. Using the Hamiltonian result we derive a new formula for the entropy of spacetimes that differs from the onequarter area law previously known for black holes. The third topic considers the AdS/CFT correspondence that hypothesizes a duality between a bulk theory on an asymptotically antide Sitter (AdS) space and a conformal field theory (CFT) on its boundary. We test this hypothesis using two different spacetimes. First, we examine rotating AdS black holes in 3, 4 and 5 dimensions whose boundary is a rotating Einstein universe of one dimension less. We find in the high temperature limit as the rotational velocity of the Einstein universe approaches the speed of light that the partition functions of the AdS spacetimes qualitatively agree with the partition functions of free scalar fields on the boundary. Second, we add nut charge to AdS space and, using the methodology derived in the second topic, we calculate the partition function. Unfortunately the boundary is a squashed three sphere and we are unable to provide a useful approximation to the partition function of a conformal field theory on this surface.
