Hoop Conjecture and the Horizon Formation Cross-Section in Kaluza-Klein Spacetimes
arXiv:0906.0689 · doi:10.1103/PhysRevD.81.024020
Abstract
We analyze momentarily static initial data sets of the gravitational field produced by two-point sources in five-dimensional Kaluza-Klein spacetimes. These initial data sets are characterized by the mass, the separation of sources and the size of a extra dimension. Using these initial data sets, we discuss the condition for black hole formation, and propose a new conjecture which is a hybrid of the four-dimensional hoop conjecture and the five-dimensional hyperhoop conjecture. By using the new conjecture, we estimate the cross section of black hole formation due to collisions of particles in Kaluza-Klein spacetimes. We show that the mass dependence of the cross section gives us information about the size and the number of the compactified extra dimensions.
25 pages, 7 figures, PRD accepted version
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- Black holes and the LHC: A review
- More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons
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