Formation of trapped surfaces in the collision of nonexpanding gravitational shock waves in an AdS4 space-time

Abstract

We discuss various mechanisms of catalysis of black holes/wormholes (BH/WH) formation in particles collisions. The current paradigm suggests that BH/WH formation in particles collisions will happen when center of mass energies of colliding particles is sufficiently above the Planck scale (the transplanckian region). To estimate the BH/WH production we use the classical geometrical cross section. We confirm the classical geometrical cross section of the BH production reconsidering the process of two transplanckian particles collision in the rest frame of one of incident particles. This consideration permits to use the standard Thorne's hoop conjecture for a matter compressed into a region to prove a variant of the conjecture dealing with a total amount of compressed energy in the case of colliding particles. We calculate geometrical cross sections for different processes and for different background, in particular, for (A)dS. We show that results are in agreement with closed trapped surface (CTS) estimations though there are no general theorems providing that the BH formation follows from CTS's formation. We show that the process of BH formation is catalyzed by the negative cosmological constant and by a particular scalar matter, namely dilaton, while it is relaxed by the positive cosmological constant and at a critical value just turns off. Also we note that the cross section is sensible to the compactification of extra dimensions and to the particular brane model.