Decoupling Limit , Lens Spaces and Taub - NUT : D = 4 Black Hole Microscopics from D = 5 Black Holes

We study the space-times of non-extremal intersecting p-brane configurations in M-theory, where one of the components in the intersection is a " NUT, " i.e. a configuration of the Taub-NUT type. Such a Taub-NUT configuration corresponds, upon compactification to D = 4, to a Gross-Perry-Sorkin (GPS) monopole. We show that in the decoupling limit of the CFT/AdS correspondence, the 4-dimensional transverse space of the NUT configuration in D = 5 is foliated by surfaces that are cyclic lens spaces S 3 /Z N , where N is the quantised monopole charge. By contrast, in D = 4 the 3-dimensional transverse space of the GPS monopole is foliated by 2-spheres. This observation provides a straightforward interpretation of the microscopics of a D = 4 string-theory black hole, with a GPS monopole as one of its constituents, in terms of the corresponding D = 5 black hole with no monopole. Using the fact that the near-horizon region of the NUT solution is a lens space, we show that if the effect of the Kaluza-Klein massive modes is neglected, p-brane configurations can be obtained from flat space-time by means of a sequence of dimensional reductions and oxidations, and U-duality transformations.