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General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE,High Energy Physics - Theory, hep-th
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.
