Black Hole Evaporation, Quantum Hair and Supertranslations

TL;DR

This paper explores the relationship between black hole hair, quantum information, and supertranslations, arguing that classical supertranslation hair does not encode interior information and that quantum dynamics govern the connection between emission and interior states.

Contribution

It demonstrates that classical supertranslation hair cannot reveal black hole interior information and emphasizes the role of quantum dynamics in encoding this information through evaporation features.

Findings

Classical supertranslation hair is distinguishable only with interior access.

Quantum dynamics link the in- and out-states of black hole evaporation.

Infrared physics plays a role in quantum state purification.

Abstract

In a black hole, hair and quantum information retrieval are interrelated phenomena. The existence of any new form of hair necessarily implies the existence of features in the quantum-mechanically evaporated radiation. Classical supertranslation hair can be only distinguished from global diffeomorphisms if we have access to the interior of the black hole. Indirect information on the interior can only be obtained from the features of the quantum evaporation. Supertranslations $(T^-,T^+) \in BMS_{-}\otimes BMS_{+}$ can be used as bookkepers of the probability distributions of the emitted quanta where the first element describes the classical injection of energy and the second one is associated to quantum-mechanical emission. The connection between $T^-$ and $T^+$ is determined by the interior quantum dynamics of the black hole. We argue that restricting to the diagonal subgroup is only possible for decoupled modes, which do not bring any non-trivial information about the black hole interior and therefore do not constitute physical hair. We show that this is also true for gravitational systems without horizon, for which both injection and emission can be described classically. Moreover, we discuss and clarify the role of infrared physics in purification.