Black Hole Time Scales: Thermalization, Infall and Complexity

Abstract

We argue that the infall time to the singularity in the interior of a black hole, is always related to a classical thermalization time. This indicates that singularities are related to the equilibration of infalling objects with the microstates of the black hole, but only in the sense of classical equilibration. When the singularity is reached, the quantum state of the black hole, initially a tensor product of the state of the infalling object and that of the black hole, is not yet a "generic" state in the enlarged Hilbert space, so its complexity is not maximal. We relate these observations to the phenomenon of mirages in the membrane paradigm description of the black hole horizon and to the shrinking of the area of causal diamonds inside the black hole. The observations are universal and we argue that they give a clue to the nature of the underlying quantum theory of black holes in all types of asymptotic space-times.