Very Long Time Scales and Black Hole Thermal Equilibrium

TL;DR

This paper investigates the long-time behavior of correlation functions in black hole spacetimes, exploring how semiclassical approximations and additional horizon dynamics relate to unitarity and information loss in quantum gravity.

Contribution

It analyzes the origin of correlation function vanishing and proposes that horizon dynamics, like a stretched horizon, are needed to explain Poincaré recurrences and unitarity.

Findings

Correlation functions vanish semiclassically due to continuum spectrum.

Including thermal gas background restores unitarity bounds.

Additional horizon configurations may resolve information-loss issues.

Abstract

We estimate the very long time behaviour of correlation functions in the presence of eternal black holes. It was pointed out by Maldacena (hep-th 0106112) that their vanishing would lead to a violation of a unitarity-based bound. The value of the bound is obtained from the holographic dual field theory. The correlators indeed vanish in a semiclassical bulk approximation. We trace the origin of their vanishing to the continuum energy spectrum in the presence of event horizons. We elaborate on the two very long time scales involved: one associated with the black hole and the other with a thermal gas in the vacuum background. We find that assigning a role to the thermal gas background, as suggested in the above work, does restore the compliance with a time-averaged unitarity bound. We also find that additional configurations are needed to explain the expected time dependence of the Poincar\'e recurrences and their magnitude. It is suggested that, while a semiclassical black hole does reproduce faithfully ``coarse grained'' properties of the system, additional dynamical features of the horizon may be necessary to resolve a finer grained information-loss problem. In particular, an effectively formed stretched horizon could yield the desired results.