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 $\phi$ 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.
Highlights
The black hole information paradox (BHIP) was put forward by Hawking in 1976 [1], which ironically seems to suggest Hawking’s own model of radiation [2,3] should be modified largely at the late time of evaporation
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 φðxaÞ naturally becomes a good label of those Maxwell soft hair degrees of freedom
This interpretation 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
Summary
The black hole information paradox (BHIP) was put forward by Hawking in 1976 [1], which ironically seems to suggest Hawking’s own model of radiation [2,3] should be modified largely at the late time of evaporation. The recent paper by Pasterski and Verlinde (PV) [16] seems to have unified the above arguments, claiming that the global soft hair beyond the no-hair theorem is the handle to reconstruct interior operators and is firewall-free They treated the supertranslation soft hair as a transition function that connects the asymptotic region and nearhorizon region, which provided a way to understand the soft hair degrees of freedom. The new ingredients here are the Page curve and the analysis of the phase space of soft hair by studying edge modes effective action Another motivation of this paper is that people are searching for free parameters [37,38,39] that label the superselection sectors inspired by island prescription and the ensemble average proposal [8,40,41]. We end with some conclusions and further comments in the last section
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