Black-hole production from ultrarelativistic collisions

Abstract. Determining the conditions under which a black hole can be produced is a long-standing and fundamental problem in general relativity. We use numerical simulations of colliding selfgravitating fluid objects to study the conditions of black-hole formation when the objects are boosted to ultrarelativistic speeds. Expanding on previous work, we show that the collision is characterized by a type-I critical behaviour, with a black hole being produced for masses above a critical value, Mc, and a partially bound object for masses below the critical one. More importantly, we show for the first time that the critical mass varies with the initial effective Lorentz factor 〈γ 〉 following a simple scaling of the type Mc ∼ K〈γ〉−1.0, thus indicating that a black hole of infinitesimal mass is produced in the limit of a diverging Lorentz factor. Furthermore, because a scaling is present also in terms of the initial stellar compactness, we provide a condition for black-hole formation in the spirit of the hoop conjecture. PACS numbers: 04.25.Dm, 04.25.dk, 04.40.Dg, 95.30.Sf, 97.60.Jd97.60.Lf 1.

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