Soft black hole information paradox: Page curve from Maxwell soft hair of a black hole

Abstract

Treating Maxwell soft hair as a transition function that relates U(1) gauge fields living in the asymptotic region and near-horizon region, the U(1) gauge parameter $\varphi$ naturally becomes a good label of those Maxwell soft hair degrees of freedom. This interpretation also builds the connection between Maxwell soft hair and U(1) edge modes living in the intermediate region, which admits a well-defined effective action description. We study the statistical properties by Euclidean path integral, which concludes that the soft hair density of state increases with black hole temperature. Hawking radiations increase black hole entropy by creating entanglements, while the measurements of soft modes project the black hole onto lower entropy states. The competition between phase spaces of Hawking radiations and soft hair measurements gives rise to one version of the Page curve consistent with the unitary evolution of the black hole.

Version published in PRD

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• Replica wormhole as a vacuum-to-vacuum transition
• Gauge theories with non-trivial boundary conditions: Black holes
• A black hole toy model with non-local and boundary modes from non-trivial boundary conditions
• Evaporating black holes and late-stage loss of soft hair
• Listening to Quantum Gravity?
• Circumventing the black hole hair-loss problem