The Information Paradox for One-sided Black Hole Evaporation in AdS

Abstract

The black hole information paradox has been troubling the minds of physicists since the discovery of Hawking radiation. The contradiction between Hawking’s result and the unitarity postulate of quantum mechanics, reached a potential resolution in favor of unitarity, with the discovery of AdS/CFT, which promised that black holes in AdS must evolve unitarily due to their dual description being manifestly unitary. However, studying the black hole information paradox in AdS can be tricky, with black holes above a certain mass being unable to evaporate due to the usual reflective boundary conditions. One particular paper that sparked hope for resolving both this evaporation issue and the information paradox, proposes a method for black hole evaporation via different boundary conditions, which allow the emitted Hawking radiation to be absorbed into an auxiliary bath. This evaporation process is shown to be unitary in the gravitational theory, with the innovative incorporation of regions behind the event horizon, which contribute to the entropy of the Hawking radiation. However, the dual description of this evaporation model is not as well-understood. In this work, we motivate the need for an auxiliary absorbing system by verifying that radiation cannot be absorbed into the holographic boundary. We review the previous work on why coupling the bath to one side of the double-sided black hole does indeed lead to one-sided black hole evaporation, and motivate why the method is unitary, at least in the gravity theory. A simple toy-model for the black hole evaporation in the dual theory is then proposed, which mimics the proposed evaporation protocol in the bulk. We show that if the bath, which is described as a local operation, acts as a unitary operator, it cannot achieve the claimed one-sided black hole evaporation. However, a non-unitary local operation of the bath has been used to derive an LOCC (Local Operations Classical Communication) operation that can achieve the one-sided black hole evaporation.