Black holes as clouded mirrors: the Hayden-Preskill protocol with symmetry.

TLDR: In this paper, the authors studied the information paradox with symmetry in the framework of the Hayden-Preskill protocol and showed that symmetry induces a delay of information leakage and an information remnant, both of which can be macroscopically large for certain initial conditions.

Abstract: The Hayden-Preskill protocol is a quantum information theoretic model of the black hole information paradox. Based on the protocol, it was revealed that information scrambling and entanglement lead to an instant leakage of information. In this paper, we study the information paradox with symmetry in the framework of the Hayden-Preskill protocol. Symmetry is an important feature of black holes that induces yet more conceptual puzzles in the regime of quantum gravity. We especially consider an axial symmetry and clarify its consequences in the information leakage problem. Using a partial decoupling approach, we first show that symmetry induces a \emph{delay} of information leakage and an \emph{information remnant}, both of which can be macroscopically large for certain initial conditions. We then clarify the physics behind the delay and the information remnant. By introducing the concept of \emph{clipping of entanglement}, we show that the delay is characterized by thermodynamic properties of the black hole associated with the symmetry. We also show that the information remnant is closely related to the symmetry-breaking of the black hole. These relations indicate the existence of non-trivial microscopic-macroscopic correspondences in the information leakage problem.