Very Long Time Scales and Black Hole Thermal Equilibrium
J. L. F. Barbon, E. Rabinovici
TL;DR
The paper investigates the very long-time behavior of correlation functions in spacetimes with eternal black holes, identifying a continuum spectrum from horizons that drives semiclassical correlators to vanish and potentially violates unitarity-based bounds. It analyzes two distinct long-time scales (black hole and thermal gas) and evaluates whether including background topologies or nonperturbative effects can restore Poincaré recurrences, finding that instanton/topology-change approaches reproduce bounds in order of magnitude but fail to capture the correct recurrence times and amplitudes. The authors argue that a purely semiclassical (master-field) description is adequate for coarse-grained thermodynamics but inadequate for fine-grained information recovery, suggesting that horizon microphysics (e.g., a stretched horizon) may be necessary to resolve information-loss puzzles. The work highlights the limitations of semiclassical gravity in addressing unitarity and points to holographic duality (AdS/CFT) as a framework where horizon dynamics could encode the needed microstructure, while noting challenges in generalizing to all spacetimes.
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 Poincaré 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.