On holographic thermalization and gravitational collapse of massless scalar fields

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 similar or equal to 1/T)> in CFT. Here T is the thermal equilibrium temperature. We study both cases with the source turned on in short (Delta t less than or similar to 1/T) and long (Delta t greater than or similar to 1/T) durations. In the former case, the thermalization time t(T) = gt/T less than or similar to 1/T and the coefficient gt similar or equal to 0.73 in the limit Delta t less than or similar to 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 similar or equal to O(1)/T.