Information Recovery From Black Holes

TL;DR

The paper argues that if black hole entropy reflects a finite set of microstates, then the black hole energy spectrum is discrete and, barring symmetries, non-degenerate, placing complete information about the state at infinity through boundary terms. In a confined (AdS-like) setting, energy and other commuting charges measured at infinity can, in principle, identify the exact microstate, though achieving the necessary Planck-scale precision requires exponentially long times. Phase information from noncommuting boundary observables allows reconstruction of general superpositions, implying no hidden interior observables in this quantum gravity framework. Practical information recovery remains challenging due to resonance-like behavior and back-reaction, but no additional physics beyond asymptotic measurements is needed to access the microstate information in principle.

Abstract

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss.