Black-hole production from ultrarelativistic collisions

TL;DR

This paper investigates black-hole formation in ultrarelativistic collisions using numerical simulations, revealing a critical mass scaling with Lorentz factor and providing a condition for black-hole production related to the hoop conjecture.

Contribution

It demonstrates for the first time that the critical mass for black-hole formation scales inversely with the Lorentz factor in ultrarelativistic collisions.

Findings

Black-hole formation exhibits type-I critical behavior.

Critical mass scales as M_c ~ K <γ>^{-1}.

A condition for black-hole formation aligns with the hoop conjecture.

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, M_c, 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 <\gamma> following a simple scaling of the type M_c ~ K <\gamma>^{-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.