Critical condition in gravitational shock wave collision and heavy ion collisions

In this paper, we derive a critical condition for matter equilibration in heavy ion collisions using a holographic approach. Gravitational shock waves with infinite transverse extension are used to model an infinite nucleus. We construct the trapped surface in the collision of two asymmetric planar shock waves with sources at different depth in the bulk AdS and formulate a critical condition for matter equilibration in the collision of "nuclei" in the dual gauge theory. We find the critical condition is insensitive to the depth of the source closer to the AdS boundary. To understand the origin of the critical condition, we compute the Next-to-Leading Order stress tensor in the boundary field theory due to the interaction of the nuclei and find that the critical condition corresponds to the breaking down of the perturbative expansion. We expect nonperturbative effects are needed to describe black hole formation.