# Black Hole Time Scales: Thermalization, Infall and Complexity

## TL;DR

This paper explores the relationship between black hole interior dynamics, thermalization, and quantum complexity, suggesting that infall times are linked to classical thermalization and that black hole singularities relate to microstate equilibration.

## Contribution

It introduces a novel connection between black hole infall times, classical thermalization, and quantum complexity, providing insights into black hole microstates and the nature of singularities.

## Key findings

- Infall time correlates with classical thermalization time.
- Black hole complexity is not maximal at the singularity.
- Universal features relate to quantum theory of black holes.

## 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.