Entanglement asymmetry study of black hole radiation

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> 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. Published by the American Physical Society 2024

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