An entanglement asymmetry study of black hole radiation

TL;DR

This paper investigates how entanglement asymmetry reveals symmetry emergence and breaking in black hole radiation, showing a transition at the Page time that impacts the understanding of black hole information dynamics.

Contribution

It introduces the use of entanglement asymmetry as a tool to study symmetry properties in black hole radiation and identifies a sharp transition at the Page time.

Findings

A $U(1)$ symmetry emerges in the radiation before the Page time.

Entanglement asymmetry exhibits a finite jump at the Page time.

Black hole symmetry appears only after the Page time.

Abstract

Hawking's discovery that black holes can evaporate through radiation emission has posed a number of questions that with time became fundamental hallmarks for a quantum theory of gravity. The most famous one is likely the information paradox, which finds an elegant explanation in the Page argument suggesting that a black hole and its radiation can be effectively represented by a random state of qubits. Leveraging the same assumption, we ponder the extent to which a black hole may display emergent symmetries, employing the entanglement asymmetry as a modern, information-based indicator of symmetry breaking. We find that for a random state devoid of any symmetry, a $U(1)$ symmetry emerges and it is exact in the thermodynamic limit before the Page time. At the Page time, the entanglement asymmetry shows a finite jump to a large value. Our findings imply that the emitted radiation is symmetric up to the Page time and then undergoes a sharp transition. Conversely the black hole is symmetric only after the Page time.