paper

Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes

arXiv:hep-th/0407050 · doi:10.1088/1126-6708/2005/01/003

Abstract

We construct and analyze a large class of exact five- and six-dimensional regular and static solutions of the vacuum Einstein equations. These solutions describe sequences of Kaluza-Klein bubbles and black holes, placed alternately so that the black holes are held apart by the bubbles. Asymptotically the solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they are part of the (μ,n) phase diagram introduced in hep-th/0309116. In particular, they occupy a hitherto unexplored region of the phase diagram, since their relative tension exceeds that of the uniform black string. The solutions contain bubbles and black holes of various topologies, including six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against gravitational collapse. We find two maps between solutions, one that relates five- and six-dimensional solutions, and another that relates solutions in the same dimension by interchanging bubbles and black holes. To illustrate the richness of the phase structure and the non-uniqueness in the (μ,n) phase diagram, we consider in detail particular examples of the general class of solutions.

71 pages, 22 figures, v2: Typos fixed, comment added in sec. 5.3

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