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Topology change in General Relativity and the black-hole black-string transition

Barak Kol
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Abstract

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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Barak Kol. 2005-10-19. Topology change in General Relativity and the black-hole black-string transition. https://doi.org/10.1088/1126-6708%2F2005%2F10%2F049

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