6.2 Hoop conjecture

An interesting use of boson stars was made by Choptuik and Pretorius [55Jump To The Next Citation Point]. They sought to answer classically whether the ultra-relativistic collision of two particles results in black-hole formation. Such a question clearly has relevance to hopes of producing black holes at the LHC (see, for example, [143, 177]). Guidance on this question is provided by Thorne’s Hoop Conjecture [213], which suggests that a black hole is formed if one squeezes energy into some spherical space of dimension less than the Schwarzschild radius for that energy.
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Figure 18: Evolutions of the head-on collisions of identical boson stars boosted toward each other with initial Lorentz factors γ as indicated. Time flows downward within each column and the top edge displays the axis of symmetry. The color-scale indicates the value of |ϕ |. In the middle frames one sees the interference pattern characteristic of high kinetic energy BS collisions (as mentioned in Figure 1View Image). In the last column on the right, the collision produces a BH with apparent horizon indicated by the black oval in the third frame. Reprinted with permission from [55Jump To The Next Citation Point]; copyright by APS.

They, therefore, numerically collide boson stars head-on at relativistic energies to study black-hole formation from just such dynamical “squeezing”. Here, the nature of boson stars is largely irrelevant as they serve as simple bundles of energy that can be accelerated (see Figure 18View Image). However, unlike using boosted black-hole solutions, the choice of boson stars avoids any type of bias or predisposition to formation of a black hole. In addition, a number of previous studies of boson star head-on collisions showed interesting interference effects at energies below the threshold for black-hole formation [49, 51, 141, 167]. Indeed, it has been proposed that such an interference pattern could be evidence for the bosonic nature of dark matter because of evidence that an ideal fluid fails to produce such a pattern [95].

Choptuik and Pretorius [55] find that indeed black-hole formation occurs at energies below that estimated by the Hoop Conjecture. This result is only a classical result consistent with the conjecture, but if it had not held, then there would have been no reason to expect a quantum theory to be consistent with it.

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