The physical mechanism of AdS instability and Holographic Thermalization

Abstract

Gravitational falling in AdS has two characteristic properties \cite{ohsin}: i) A thick shell becomes a thin shell. ii) Any shape become spherical. Such focusing character of AdS, for the collapse of dusts, leads to the rapid thermalization mechanism in strongly interacting system. For the collapse of a wave, it explains the cascade of energy to UV through repeated bounces, which has been extensively discussed in recent numerical works. Therefore the focusing is the physical mechanism of instability of AdS. Such sharp contrast between the dust and wave in collapse, together with the experimental observation of rapid thermalization, suggest that the initial condition of created particles in RHIC is in a state with random character rather than a coherent one. Two time scales, one for thermalization and the other for hydro-nization are defined and calculated in terms of the total mass density and energy distribution of the initial particles. We find $t_{th}\sim (1-c_1/E^2)^{1/2}/T $ so that softer modes thermalize earlier. However, for hydro-nization, $t_{hyd} \sim 1/E^{2/3}T^{1/3}$ therefore harder modes come earlier. We also show that near horizon limit of Dp brane solutions have similar focusing effect which is enough to guarantee the early thermalization.