Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-06-24
JHEP 0510 (2005) 049
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, 13 figures, v2: minor changes, v3: published version. See "Note added" at end of introduction
Scientific paper
10.1088/1126-6708/2005/10/049
In the presence of compact dimensions massive solutions of General Relativity may take one of several forms including the black-hole and the black-string, the simplest relevant background being R^{3+1} * S^1. It is shown how Morse theory places constraints on the qualitative features of the phase diagram, and a minimalistic diagram is suggested which describes a first order transition whose only stable phases are the uniform string and the black-hole. The diagram calls for a topology changing ``merger'' transition in which the black-hole evolves continuously into an unstable black-string phase. As evidence a local model for the transition is presented in which the cone over S^2 * S^2 plays a central role. Horizon cusps do not appear as precursors to black hole merger. A generalization to higher dimensions finds that whereas the cone has a tachyon function for d=5, its stability depends interestingly on the dimension - it is unstable for d<10, and stable for d>10.
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