Hoop Conjecture and the Horizon Formation Cross-Section in Kaluza-Klein Spacetimes

Details Hoop Conjecture and the Horizon Formation Cross-Section in Kaluza-Klein Spacetimes Hoop Conjecture and the Horizon Formation Cross-Section in Kaluza-Klein Spacetimes

2009-06-03

arxiv.org/abs/0906.0689v3

Phys.Rev.D81:024020,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, 7 figures, PRD accepted version

Scientific paper

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.

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