Before the Page Time: Maximum Entanglements or the Return of the Monster?

Abstract

The conservation of information of evaporating black holes is a very natural consequence of unitarity, which is the fundamental symmetry of quantum mechanics. In order to study the conservation of information, we need to understand the nature of the entanglement entropy. The entropy of Hawking radiation is approximately equal to the maximum of entanglement entropy if a black hole is in a state before the Page time, i.e., when the entropy of Hawking radiation is smaller than the entropy of the black hole. However, if there exists a process generating smaller entanglements rather than maximal entanglements, the entropy of Hawking radiation will become smaller than the maximum of the entanglement entropy before the Page time. If this process accumulates, even though the probability is small, the emitted radiation can eventually be distinguished from the exactly thermal state. In this paper, we provide several interpretations of this phenomenon: (1) information of the collapsed matter emitted before the Page time, (2) there exists a firewall or a non-local effect before the Page time, or (3) the statistical entropy is greater than the areal entropy; a monster is formed. Our conclusion will help resolve the information loss paradox by providing groundwork for further research.

Page curve of AdS-Vaidya model for evaporating black holes

“…There were many proposals to try and alleviate the issues posed by the information paradox [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Among the proposals, one route that has taken much attention is through the Ryu and Takayanagi (RT) prescription which studies the fine-grained entropy in a geometrical context through the AdS/CFT correspondence, albeit only for time-independent cases [23,24].…”