In asymptotically flat space a rotating black hole cannot be in thermodynamic equilibrium because the thermal radiation would have to be co-rotating faster than light far from the black hole. However in asymptotically anti-de Sitter space such equilibrium is possible for certain ranges of the parameters. We examine the relationship between conformal field theory in rotating Einstein universes of dimensions two to four and Kerr anti-de Sitter black holes in dimensions three to five. The five dimensional solution is new. We find similar divergences in the partition function of the conformal field theory and the action of the black hole at the critical angular velocity at which the Einstein rotates at the speed of light. This should be an interesting limit in which to study large N Yang-Mills.

It has been proposed that spacetimes with a U (1) isometry group have contributions to the entropy from Misner strings as well as from the area of d − 2 dimensional fixed point sets. In this paper we test this proposal by constructing Taub-Nut-AdS and Taub-Bolt-AdS solutions which are examples of a new class of asymptotically locally anti-de Sitter spaces. We find that with the additional contribution from the Misner strings, we exactly reproduce the entropy calculated from the action by the usual thermodynamic relations. This entropy has the right parameter dependence to agree with the entropy of a conformal field theory on the boundary, which is a squashed three-sphere, at least in the limit of large squashing. However the conformal field theory and the normalisation of the entropy remain to be determined.

An understanding of developmental biology can provide useful insights into how different tissue-engineered repairs might be designed. During embryogenesis of the intervertebral disk, the cells of the notochord play a critical role in initiating tissue formation, and may be responsible for development of the nucleus pulposus. In some species, including humans, these notochordal cells may eventually be lost, either through apoptosis or terminal differentiation, and are replaced by chondrocyte-like cells. However, there is some evidence that the notochordal cells may persist in at least some humans. This review discusses some of the potential applications of notochordal cells in tissue engineering of the nucleus pulposus.

The nuclei pulposi of the intervertebral discs (IVDs) contain a mixed population of cell types at various stages of maturation. This tissue is formed either by or with the help of cells from the embryonic notochord, which appear to be replaced during development by a population of chondrocyte-like cells of uncertain origin. However, this transition occurs at widely varying times, depending upon the species -or even breed -of the animal being examined. There is considerable debate among spine researchers as to whether the presence of these residual notochordal cells has a significant impact upon IVD degeneration models, and thus which models may best represent the human condition. The present study examines several different species commonly used in lumbar spine investigations to explore the variability of notochordal cells in the IVD.