On holographic thermalization and gravitational collapse of massless scalar fields

Abstract

In this paper we study thermalization in a strongly coupled system via AdS/CFT. Initially, the energy is injected into the system by turning on a spatially homogenous scalar source coupled to a marginal composite operator. The thermalization process is studied by numerically solving Einstein's equations coupled to a massless scalar field in the Poincare patch of AdS_5. We define a thermalization time t_T on the AdS side, which has an interpretation in terms of a spacelike Wilson loop <W(l =1/T)> in CFT. Here T is the thermal equilibrium temperature. We study both cases with the source turned on in short(Delta t <= 1/T) and long(Delta t >= 1/T) durations. In the former case, the thermalization time t_T = g_t/T <= 1/T and the coefficient g_t = 0.73 in the limit Delta t <= 0.02/T. In the latter case, we find double- and multiple-collapse solutions, which may be interpreted as the gravity duals of two- or multi-stage thermalization in CFT. In all the cases our results indicate that such a strongly coupled system thermalizes in a typical time scale t_T=O(1)/T.