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

By B. Kol. 2002

161 citations recorded by the source corpus.

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 3+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 × S2 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/71d7d322b8af56a62fc06326204fc6cadca93b90

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Citations in the corpus

Mimicking the QCD equation of state with a dual black hole (2008, background): “Considerable work has been devoted to the question of what the endpoint of the evolution of the Gregory-Laflamme instability might be: see for example [26, 27, 28, 29, 30, 31].”
A new approach to static numerical relativity and its application to Kaluza–Klein black holes (2009, methodology): “The second is the continuation of the zero mode at the branching point into a negative mode, agreeing with the Morse theory picture of Kol [15, 88].”
The Phase Structure of Higher-Dimensional Black Rings and Black Holes (2007, background): “It would be interesting to study whether the merger happens through a conical geometry, like [50, 51, 52, 33] have argued for non-uniform black string/membrane phases.”
Non-relativistic gravitation: from Newton to Einstein and back (2007, methodology): “Caged black holes were previously analyzed by means of Matched Asymptotic Expansion (MAE) [3, 4, 5, 6] due to their part in the black-hole black-string phase transition [7, 8, 9] associated with the black string instability of Gregory-Laflamme [10].”
The phase transition between caged black holes and black strings (2004, methodology): “As we mentioned above, to determine the order there is a somewhat more efficient method, namely it is actually enough to compute only the second order back-reaction and substitute into the quartic part of the action (see appendix A in [44] and [18]).”