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

TL;DR

This paper investigates black hole formation in five-dimensional Kaluza-Klein spacetimes, proposing a new hybrid conjecture to estimate the cross section of black hole formation from particle collisions, revealing insights into extra dimensions.

Contribution

It introduces a new hybrid conjecture combining the hoop and hyperhoop conjectures to analyze black hole formation in higher-dimensional spacetimes.

Findings

Derived a condition for black hole formation in Kaluza-Klein spacetimes.

Estimated black hole formation cross sections based on the new conjecture.

Revealed how cross section dependence on mass informs about extra dimensions.

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.