Topology change in general relativity, and the black-hole black-string transition

Barak Kol*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


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 ℝ3+1 × S1. 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 S2 × 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.

Original languageAmerican English
Pages (from-to)1245-1273
Number of pages29
JournalJournal of High Energy Physics
Issue number10
StatePublished - 1 Oct 2005


  • Black Holes
  • Classical Theories of Gravity


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